## com.google.common.collect
Class Sets

    java.lang.Object
      com.google.common.collect.Sets

    @GwtCompatible(emulated=true)
    public final class Sets

extends Object

Static utility methods pertaining to `Set` instances. Also see this class's counterparts `Lists` and `Maps`.

See the Guava User Guide article on `Sets`.

Since:
  2.0 (imported from Google Collections Library)
Author:
  Kevin Bourrillion, Jared Levy, Chris Povirk

Nested Class Summary
`static class` `Sets.SetView<E>` An unmodifiable view of a set which may be backed by other sets; this view will change as the backing sets do.

Method Summary

`static

`<B> Set<List<B>>`

`

`cartesianProduct(List<? extends Set<? extends B>> sets)`
Returns every possible list that can be formed by choosing one element from each of the given sets in order; the "n-ary Cartesian product" of the sets.

`static

`<B> Set<List<B>>`

`

`cartesianProduct(Set<? extends B>... sets)`
Returns every possible list that can be formed by choosing one element from each of the given sets in order; the "n-ary Cartesian product" of the sets.

`static

`<E extends Enum<E>> EnumSet<E>`

`

`complementOf(Collection<E> collection)`
Creates an `EnumSet` consisting of all enum values that are not in the specified collection.

`static

`<E extends Enum<E>> EnumSet<E>`

`

`complementOf(Collection<E> collection, Class<E> type)`
Creates an `EnumSet` consisting of all enum values that are not in the specified collection.

`static

`<E> Sets.SetView<E>`

`

`difference(Set<E> set1, Set<?> set2)`
Returns an unmodifiable view of the difference of two sets.

`static

`<E> Set<E>`

`

`filter(Set<E> unfiltered, Predicate<? super E> predicate)`
Returns the elements of `unfiltered` that satisfy a predicate.

`static

`<E> SortedSet<E>`

`

`filter(SortedSet<E> unfiltered, Predicate<? super E> predicate)`
Returns the elements of a `SortedSet`, `unfiltered`, that satisfy a predicate.

`static

`<E extends Enum<E>> ImmutableSet<E>`

`

`immutableEnumSet(E anElement, E... otherElements)`
Returns an immutable set instance containing the given enum elements.

`static

`<E extends Enum<E>> ImmutableSet<E>`

`

`immutableEnumSet(Iterable<E> elements)`
Returns an immutable set instance containing the given enum elements.

`static

`<E> Sets.SetView<E>`

`

`intersection(Set<E> set1, Set<?> set2)`
Returns an unmodifiable view of the intersection of two sets.

`static

`<E> CopyOnWriteArraySet<E>`

`

`newCopyOnWriteArraySet()`
Creates an empty `CopyOnWriteArraySet` instance.

`static

`<E> CopyOnWriteArraySet<E>`

`

`newCopyOnWriteArraySet(Iterable<? extends E> elements)`
Creates a `CopyOnWriteArraySet` instance containing the given elements.

`static

`<E extends Enum<E>> EnumSet<E>`

`

`newEnumSet(Iterable<E> iterable, Class<E> elementType)`
Returns a new `EnumSet` instance containing the given elements.

`static

`<E> HashSet<E>`

`

`newHashSet()`
Creates a mutable, empty `HashSet` instance.

`static

`<E> HashSet<E>`

`

`newHashSet(E... elements)`
Creates a mutable `HashSet` instance containing the given elements in unspecified order.

`static

`<E> HashSet<E>`

`

`newHashSet(Iterable<? extends E> elements)`
Creates a mutable `HashSet` instance containing the given elements in unspecified order.

`static

`<E> HashSet<E>`

`

`newHashSet(Iterator<? extends E> elements)`
Creates a mutable `HashSet` instance containing the given elements in unspecified order.

`static

`<E> HashSet<E>`

`

`newHashSetWithExpectedSize(int expectedSize)`
Creates a `HashSet` instance, with a high enough "initial capacity" that it should hold `expectedSize` elements without growth.

`static

`<E> Set<E>`

`

`newIdentityHashSet()`
Creates an empty `Set` that uses identity to determine equality.

`static

`<E> LinkedHashSet<E>`

`

`newLinkedHashSet()`
Creates a mutable, empty `LinkedHashSet` instance.

`static

`<E> LinkedHashSet<E>`

`

`newLinkedHashSet(Iterable<? extends E> elements)`
Creates a mutable `LinkedHashSet` instance containing the given elements in order.

`static

`<E> LinkedHashSet<E>`

`

`newLinkedHashSetWithExpectedSize(int expectedSize)`
Creates a `LinkedHashSet` instance, with a high enough "initial capacity" that it should hold `expectedSize` elements without growth.

`static

`<E> Set<E>`

`

`newSetFromMap(Map<E,Boolean> map)`
Returns a set backed by the specified map.

`static

`<E extends Comparable> TreeSet<E>`

`

`newTreeSet()`
Creates a mutable, empty `TreeSet` instance sorted by the natural sort ordering of its elements.

`static

`<E> TreeSet<E>`

`

`newTreeSet(Comparator<? super E> comparator)`
Creates a mutable, empty `TreeSet` instance with the given comparator.

`static

`<E extends Comparable> TreeSet<E>`

`

`newTreeSet(Iterable<? extends E> elements)`
Creates a mutable `TreeSet` instance containing the given elements sorted by their natural ordering.

`static

`<E> Set<Set<E>>`

`

`powerSet(Set<E> set)`
Returns the set of all possible subsets of `set`.

`static

`<E> Sets.SetView<E>`

`

`symmetricDifference(Set<? extends E> set1, Set<? extends E> set2)`
Returns an unmodifiable view of the symmetric difference of two sets.

`static

`<E> NavigableSet<E>`

`

`synchronizedNavigableSet(NavigableSet<E> navigableSet)`
Returns a synchronized (thread-safe) navigable set backed by the specified navigable set.

`static

`<E> Sets.SetView<E>`

`

`union(Set<? extends E> set1, Set<? extends E> set2)`
Returns an unmodifiable view of the union of two sets.

`static

`<E> NavigableSet<E>`

`

`unmodifiableNavigableSet(NavigableSet<E> set)`
Returns an unmodifiable view of the specified navigable set.

Methods inherited from class java.lang.Object
`clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`

Method Detail

### immutableEnumSet

    @GwtCompatible(serializable=true)
    public static <E extends Enum<E>> ImmutableSet<E> immutableEnumSet(E anElement,
                                                                                                 E... otherElements)

  Returns an immutable set instance containing the given enum elements. Internally, the returned set will be backed by an `EnumSet`.

  The iteration order of the returned set follows the enum's iteration order, not the order in which the elements are provided to the method.

  Parameters:
    `anElement` - one of the elements the set should contain
    `otherElements` - the rest of the elements the set should contain
  Returns:
    an immutable set containing those elements, minus duplicates

### immutableEnumSet

    @GwtCompatible(serializable=true)
    public static <E extends Enum<E>> ImmutableSet<E> immutableEnumSet(Iterable<E> elements)

  Returns an immutable set instance containing the given enum elements. Internally, the returned set will be backed by an `EnumSet`.

  The iteration order of the returned set follows the enum's iteration order, not the order in which the elements appear in the given collection.

  Parameters:
    `elements` - the elements, all of the same `enum` type, that the set should contain
  Returns:
    an immutable set containing those elements, minus duplicates

### newEnumSet

    public static <E extends Enum<E>> EnumSet<E> newEnumSet(Iterable<E> iterable,
                                                            Class<E> elementType)

  Returns a new `EnumSet` instance containing the given elements. Unlike `EnumSet.copyOf(Collection)`, this method does not produce an exception on an empty collection, and it may be called on any iterable, not just a `Collection`.

### newHashSet

    public static <E> HashSet<E> newHashSet()

  Creates a mutable, empty `HashSet` instance.

  Note: if mutability is not required, use `ImmutableSet.of()` instead.

  Note: if `E` is an `Enum` type, use `EnumSet.noneOf(java.lang.Class<E>)` instead.

  Returns:
    a new, empty `HashSet`

### newHashSet

    public static <E> HashSet<E> newHashSet(E... elements)

  Creates a mutable `HashSet` instance containing the given elements in unspecified order.

  Note: if mutability is not required and the elements are non-null, use an overload of `ImmutableSet.of()` (for varargs) or `ImmutableSet.copyOf(Object[])` (for an array) instead.

  Note: if `E` is an `Enum` type, use `EnumSet.of(Enum, Enum[])` instead.

  Parameters:
    `elements` - the elements that the set should contain
  Returns:
    a new `HashSet` containing those elements (minus duplicates)

### newHashSetWithExpectedSize

    public static <E> HashSet<E> newHashSetWithExpectedSize(int expectedSize)

  Creates a `HashSet` instance, with a high enough "initial capacity" that it should hold `expectedSize` elements without growth. This behavior cannot be broadly guaranteed, but it is observed to be true for OpenJDK 1.6. It also can't be guaranteed that the method isn't inadvertently oversizing the returned set.

  Parameters:
    `expectedSize` - the number of elements you expect to add to the returned set
  Returns:
    a new, empty `HashSet` with enough capacity to hold `expectedSize` elements without resizing
  Throws:
    `IllegalArgumentException` - if `expectedSize` is negative

### newHashSet

    public static <E> HashSet<E> newHashSet(Iterable<? extends E> elements)

  Creates a mutable `HashSet` instance containing the given elements in unspecified order.

  Note: if mutability is not required and the elements are non-null, use `ImmutableSet.copyOf(Iterable)` instead.

  Note: if `E` is an `Enum` type, use `newEnumSet(Iterable, Class)` instead.

  Parameters:
    `elements` - the elements that the set should contain
  Returns:
    a new `HashSet` containing those elements (minus duplicates)

### newHashSet

    public static <E> HashSet<E> newHashSet(Iterator<? extends E> elements)

  Creates a mutable `HashSet` instance containing the given elements in unspecified order.

  Note: if mutability is not required and the elements are non-null, use `ImmutableSet.copyOf(Iterable)` instead.

  Note: if `E` is an `Enum` type, you should create an `EnumSet` instead.

  Parameters:
    `elements` - the elements that the set should contain
  Returns:
    a new `HashSet` containing those elements (minus duplicates)

### newLinkedHashSet

    public static <E> LinkedHashSet<E> newLinkedHashSet()

  Creates a mutable, empty `LinkedHashSet` instance.

  Note: if mutability is not required, use `ImmutableSet.of()` instead.

  Returns:
    a new, empty `LinkedHashSet`

### newLinkedHashSetWithExpectedSize

    public static <E> LinkedHashSet<E> newLinkedHashSetWithExpectedSize(int expectedSize)

  Creates a `LinkedHashSet` instance, with a high enough "initial capacity" that it should hold `expectedSize` elements without growth. This behavior cannot be broadly guaranteed, but it is observed to be true for OpenJDK 1.6. It also can't be guaranteed that the method isn't inadvertently oversizing the returned set.

  Parameters:
    `expectedSize` - the number of elements you expect to add to the returned set
  Returns:
    a new, empty `LinkedHashSet` with enough capacity to hold `expectedSize` elements without resizing
  Throws:
    `IllegalArgumentException` - if `expectedSize` is negative
  Since:
    11.0

### newLinkedHashSet

    public static <E> LinkedHashSet<E> newLinkedHashSet(Iterable<? extends E> elements)

  Creates a mutable `LinkedHashSet` instance containing the given elements in order.

  Note: if mutability is not required and the elements are non-null, use `ImmutableSet.copyOf(Iterable)` instead.

  Parameters:
    `elements` - the elements that the set should contain, in order
  Returns:
    a new `LinkedHashSet` containing those elements (minus duplicates)

### newTreeSet

    public static <E extends Comparable> TreeSet<E> newTreeSet()

  Creates a mutable, empty `TreeSet` instance sorted by the natural sort ordering of its elements.

  Note: if mutability is not required, use `ImmutableSortedSet.of()` instead.

  Returns:
    a new, empty `TreeSet`

### newTreeSet

    public static <E extends Comparable> TreeSet<E> newTreeSet(Iterable<? extends E> elements)

  Creates a mutable `TreeSet` instance containing the given elements sorted by their natural ordering.

  Note: if mutability is not required, use `ImmutableSortedSet.copyOf(Iterable)` instead.

  Note: If `elements` is a `SortedSet` with an explicit comparator, this method has different behavior than `TreeSet.TreeSet(SortedSet)`, which returns a `TreeSet` with that comparator.

  Parameters:
    `elements` - the elements that the set should contain
  Returns:
    a new `TreeSet` containing those elements (minus duplicates)

### newTreeSet

    public static <E> TreeSet<E> newTreeSet(Comparator<? super E> comparator)

  Creates a mutable, empty `TreeSet` instance with the given comparator.

  Note: if mutability is not required, use `ImmutableSortedSet.orderedBy(comparator).build()` instead.

  Parameters:
    `comparator` - the comparator to use to sort the set
  Returns:
    a new, empty `TreeSet`
  Throws:
    `NullPointerException` - if `comparator` is null

### newIdentityHashSet

    public static <E> Set<E> newIdentityHashSet()

  Creates an empty `Set` that uses identity to determine equality. It compares object references, instead of calling `equals`, to determine whether a provided object matches an element in the set. For example, `contains` returns `false` when passed an object that equals a set member, but isn't the same instance. This behavior is similar to the way `IdentityHashMap` handles key lookups.

  Since:
    8.0

### newCopyOnWriteArraySet

    @GwtIncompatible(value="CopyOnWriteArraySet")
    public static <E> CopyOnWriteArraySet<E> newCopyOnWriteArraySet()

  Creates an empty `CopyOnWriteArraySet` instance.

  Note: if you need an immutable empty `Set`, use `Collections.emptySet()` instead.

  Returns:
    a new, empty `CopyOnWriteArraySet`
  Since:
    12.0

### newCopyOnWriteArraySet

    @GwtIncompatible(value="CopyOnWriteArraySet")
    public static <E> CopyOnWriteArraySet<E> newCopyOnWriteArraySet(Iterable<? extends E> elements)

  Creates a `CopyOnWriteArraySet` instance containing the given elements.

  Parameters:
    `elements` - the elements that the set should contain, in order
  Returns:
    a new `CopyOnWriteArraySet` containing those elements
  Since:
    12.0

### complementOf

    public static <E extends Enum<E>> EnumSet<E> complementOf(Collection<E> collection)

  Creates an `EnumSet` consisting of all enum values that are not in the specified collection. If the collection is an `EnumSet`, this method has the same behavior as `EnumSet.complementOf(java.util.EnumSet<E>)`. Otherwise, the specified collection must contain at least one element, in order to determine the element type. If the collection could be empty, use `complementOf(Collection, Class)` instead of this method.

  Parameters:
    `collection` - the collection whose complement should be stored in the enum set
  Returns:
    a new, modifiable `EnumSet` containing all values of the enum that aren't present in the given collection
  Throws:
    `IllegalArgumentException` - if `collection` is not an `EnumSet` instance and contains no elements

### complementOf

    public static <E extends Enum<E>> EnumSet<E> complementOf(Collection<E> collection,
                                                              Class<E> type)

  Creates an `EnumSet` consisting of all enum values that are not in the specified collection. This is equivalent to `EnumSet.complementOf(java.util.EnumSet<E>)`, but can act on any input collection, as long as the elements are of enum type.

  Parameters:
    `collection` - the collection whose complement should be stored in the `EnumSet`
    `type` - the type of the elements in the set
  Returns:
    a new, modifiable `EnumSet` initially containing all the values of the enum not present in the given collection

### newSetFromMap

    public static <E> Set<E> newSetFromMap(Map<E,Boolean> map)

  Returns a set backed by the specified map. The resulting set displays the same ordering, concurrency, and performance characteristics as the backing map. In essence, this factory method provides a `Set` implementation corresponding to any `Map` implementation. There is no need to use this method on a `Map` implementation that already has a corresponding `Set` implementation (such as `HashMap` or `TreeMap`).

  Each method invocation on the set returned by this method results in exactly one method invocation on the backing map or its `keySet` view, with one exception. The `addAll` method is implemented as a sequence of `put` invocations on the backing map.

  The specified map must be empty at the time this method is invoked, and should not be accessed directly after this method returns. These conditions are ensured if the map is created empty, passed directly to this method, and no reference to the map is retained, as illustrated in the following code fragment:

        Set<Object> identityHashSet = Sets.newSetFromMap(
             new IdentityHashMap<Object, Boolean>());

  This method has the same behavior as the JDK 6 method `Collections.newSetFromMap()`. The returned set is serializable if the backing map is.

  Parameters:
    `map` - the backing map
  Returns:
    the set backed by the map
  Throws:
    `IllegalArgumentException` - if `map` is not empty

### union

    public static <E> Sets.SetView<E> union(Set<? extends E> set1,
                                            Set<? extends E> set2)

  Returns an unmodifiable view of the union of two sets. The returned set contains all elements that are contained in either backing set. Iterating over the returned set iterates first over all the elements of `set1`, then over each element of `set2`, in order, that is not contained in `set1`.

  Results are undefined if `set1` and `set2` are sets based on different equivalence relations (as `HashSet`, `TreeSet`, and the `Map.keySet()` of an `IdentityHashMap` all are).

  Note: The returned view performs better when `set1` is the smaller of the two sets. If you have reason to believe one of your sets will generally be smaller than the other, pass it first.

  Further, note that the current implementation is not suitable for nested `union` views, i.e. the following should be avoided when in a loop: `union = Sets.union(union, anotherSet);`, since iterating over the resulting set has a cubic complexity to the depth of the nesting.

### intersection

    public static <E> Sets.SetView<E> intersection(Set<E> set1,
                                                   Set<?> set2)

  Returns an unmodifiable view of the intersection of two sets. The returned set contains all elements that are contained by both backing sets. The iteration order of the returned set matches that of `set1`.

  Results are undefined if `set1` and `set2` are sets based on different equivalence relations (as `HashSet`, `TreeSet`, and the keySet of an `IdentityHashMap` all are).

  Note: The returned view performs slightly better when `set1` is the smaller of the two sets. If you have reason to believe one of your sets will generally be smaller than the other, pass it first. Unfortunately, since this method sets the generic type of the returned set based on the type of the first set passed, this could in rare cases force you to make a cast, for example:

         Set<Object> aFewBadObjects = ...
         Set<String> manyBadStrings = ...

         // impossible for a non-String to be in the intersection
         SuppressWarnings("unchecked")
         Set<String> badStrings = (Set) Sets.intersection(
             aFewBadObjects, manyBadStrings);

  This is unfortunate, but should come up only very rarely.

### difference

    public static <E> Sets.SetView<E> difference(Set<E> set1,
                                                 Set<?> set2)

  Returns an unmodifiable view of the difference of two sets. The returned set contains all elements that are contained by `set1` and not contained by `set2`. `set2` may also contain elements not present in `set1`; these are simply ignored. The iteration order of the returned set matches that of `set1`.

  Results are undefined if `set1` and `set2` are sets based on different equivalence relations (as `HashSet`, `TreeSet`, and the keySet of an `IdentityHashMap` all are).

### symmetricDifference

    public static <E> Sets.SetView<E> symmetricDifference(Set<? extends E> set1,
                                                          Set<? extends E> set2)

  Returns an unmodifiable view of the symmetric difference of two sets. The returned set contains all elements that are contained in either `set1` or `set2` but not in both. The iteration order of the returned set is undefined.

  Results are undefined if `set1` and `set2` are sets based on different equivalence relations (as `HashSet`, `TreeSet`, and the keySet of an `IdentityHashMap` all are).

  Since:
    3.0

### filter

    public static <E> Set<E> filter(Set<E> unfiltered,
                                    Predicate<? super E> predicate)

  Returns the elements of `unfiltered` that satisfy a predicate. The returned set is a live view of `unfiltered`; changes to one affect the other.

  The resulting set's iterator does not support `remove()`, but all other set methods are supported. When given an element that doesn't satisfy the predicate, the set's `add()` and `addAll()` methods throw an `IllegalArgumentException`. When methods such as `removeAll()` and `clear()` are called on the filtered set, only elements that satisfy the filter will be removed from the underlying set.

  The returned set isn't threadsafe or serializable, even if `unfiltered` is.

  Many of the filtered set's methods, such as `size()`, iterate across every element in the underlying set and determine which elements satisfy the filter. When a live view is not needed, it may be faster to copy `Iterables.filter(unfiltered, predicate)` and use the copy.

  Warning: `predicate` must be consistent with equals, as documented at `Predicate.apply(T)`. Do not provide a predicate such as `Predicates.instanceOf(ArrayList.class)`, which is inconsistent with equals. (See `Iterables.filter(Iterable, Class)` for related functionality.)

### filter

    public static <E> SortedSet<E> filter(SortedSet<E> unfiltered,
                                          Predicate<? super E> predicate)

  Returns the elements of a `SortedSet`, `unfiltered`, that satisfy a predicate. The returned set is a live view of `unfiltered`; changes to one affect the other.

  The resulting set's iterator does not support `remove()`, but all other set methods are supported. When given an element that doesn't satisfy the predicate, the set's `add()` and `addAll()` methods throw an `IllegalArgumentException`. When methods such as `removeAll()` and `clear()` are called on the filtered set, only elements that satisfy the filter will be removed from the underlying set.

  The returned set isn't threadsafe or serializable, even if `unfiltered` is.

  Many of the filtered set's methods, such as `size()`, iterate across every element in the underlying set and determine which elements satisfy the filter. When a live view is not needed, it may be faster to copy `Iterables.filter(unfiltered, predicate)` and use the copy.

  Warning: `predicate` must be consistent with equals, as documented at `Predicate.apply(T)`. Do not provide a predicate such as `Predicates.instanceOf(ArrayList.class)`, which is inconsistent with equals. (See `Iterables.filter(Iterable, Class)` for related functionality.)

  Since:
    11.0

### cartesianProduct

    public static <B> Set<List<B>> cartesianProduct(List<? extends Set<? extends B>> sets)

  Returns every possible list that can be formed by choosing one element from each of the given sets in order; the "n-ary Cartesian product" of the sets. For example:

         Sets.cartesianProduct(ImmutableList.of(
             ImmutableSet.of(1, 2),
             ImmutableSet.of("A", "B", "C")))

  returns a set containing six lists:
  - `ImmutableList.of(1, "A")`
  - `ImmutableList.of(1, "B")`
  - `ImmutableList.of(1, "C")`
  - `ImmutableList.of(2, "A")`
  - `ImmutableList.of(2, "B")`
  - `ImmutableList.of(2, "C")`
  The order in which these lists are returned is not guaranteed, however the position of an element inside a tuple always corresponds to the position of the set from which it came in the input list. Note that if any input set is empty, the Cartesian product will also be empty. If no sets at all are provided (an empty list), the resulting Cartesian product has one element, an empty list (counter-intuitive, but mathematically consistent).

  Performance notes: while the cartesian product of sets of size `m, n, p` is a set of size `m x n x p`, its actual memory consumption is much smaller. When the cartesian set is constructed, the input sets are merely copied. Only as the resulting set is iterated are the individual lists created, and these are not retained after iteration.

  Type Parameters:
    `B` - any common base class shared by all axes (often just `Object`)
  Parameters:
    `sets` - the sets to choose elements from, in the order that the elements chosen from those sets should appear in the resulting lists
  Returns:
    the Cartesian product, as an immutable set containing immutable lists
  Throws:
    `NullPointerException` - if `sets`, any one of the `sets`, or any element of a provided set is null
  Since:
    2.0

### cartesianProduct

    public static <B> Set<List<B>> cartesianProduct(Set<? extends B>... sets)

  Returns every possible list that can be formed by choosing one element from each of the given sets in order; the "n-ary Cartesian product" of the sets. For example:

         Sets.cartesianProduct(
             ImmutableSet.of(1, 2),
             ImmutableSet.of("A", "B", "C"))

  returns a set containing six lists:
  - `ImmutableList.of(1, "A")`
  - `ImmutableList.of(1, "B")`
  - `ImmutableList.of(1, "C")`
  - `ImmutableList.of(2, "A")`
  - `ImmutableList.of(2, "B")`
  - `ImmutableList.of(2, "C")`
  The order in which these lists are returned is not guaranteed, however the position of an element inside a tuple always corresponds to the position of the set from which it came in the input list. Note that if any input set is empty, the Cartesian product will also be empty. If no sets at all are provided, the resulting Cartesian product has one element, an empty list (counter-intuitive, but mathematically consistent).

  Performance notes: while the cartesian product of sets of size `m, n, p` is a set of size `m x n x p`, its actual memory consumption is much smaller. When the cartesian set is constructed, the input sets are merely copied. Only as the resulting set is iterated are the individual lists created, and these are not retained after iteration.

  Type Parameters:
    `B` - any common base class shared by all axes (often just `Object`)
  Parameters:
    `sets` - the sets to choose elements from, in the order that the elements chosen from those sets should appear in the resulting lists
  Returns:
    the Cartesian product, as an immutable set containing immutable lists
  Throws:
    `NullPointerException` - if `sets`, any one of the `sets`, or any element of a provided set is null
  Since:
    2.0

### powerSet

    @GwtCompatible(serializable=false)
    public static <E> Set<Set<E>> powerSet(Set<E> set)

  Returns the set of all possible subsets of `set`. For example, `powerSet(ImmutableSet.of(1, 2))` returns the set `{{}, {1}, {2}, {1, 2}}`.

  Elements appear in these subsets in the same iteration order as they appeared in the input set. The order in which these subsets appear in the outer set is undefined. Note that the power set of the empty set is not the empty set, but a one-element set containing the empty set.

  The returned set and its constituent sets use `equals` to decide whether two elements are identical, even if the input set uses a different concept of equivalence.

  Performance notes: while the power set of a set with size `n` is of size `2^n`, its memory usage is only `O(n)`. When the power set is constructed, the input set is merely copied. Only as the power set is iterated are the individual subsets created, and these subsets themselves occupy only a few bytes of memory regardless of their size.

  Parameters:
    `set` - the set of elements to construct a power set from
  Returns:
    the power set, as an immutable set of immutable sets
  Throws:
    `IllegalArgumentException` - if `set` has more than 30 unique elements (causing the power set size to exceed the `int` range)
    `NullPointerException` - if `set` is or contains `null`
  Since:
    4.0
  See Also:
    Power set article at Wikipedia

### unmodifiableNavigableSet

    @GwtIncompatible(value="NavigableSet")
    public static <E> NavigableSet<E> unmodifiableNavigableSet(NavigableSet<E> set)

  Returns an unmodifiable view of the specified navigable set. This method allows modules to provide users with "read-only" access to internal navigable sets. Query operations on the returned set "read through" to the specified set, and attempts to modify the returned set, whether direct or via its collection views, result in an `UnsupportedOperationException`.

  The returned navigable set will be serializable if the specified navigable set is serializable.

  Parameters:
    `set` - the navigable set for which an unmodifiable view is to be returned
  Returns:
    an unmodifiable view of the specified navigable set
  Since:
    12.0

### synchronizedNavigableSet

    @Beta
    @GwtIncompatible(value="NavigableSet")
    public static <E> NavigableSet<E> synchronizedNavigableSet(NavigableSet<E> navigableSet)

  Returns a synchronized (thread-safe) navigable set backed by the specified navigable set. In order to guarantee serial access, it is critical that all access to the backing navigable set is accomplished through the returned navigable set (or its views).

  It is imperative that the user manually synchronize on the returned sorted set when iterating over it or any of its `descendingSet`, `subSet`, `headSet`, or `tailSet` views.

         NavigableSet<E> set = synchronizedNavigableSet(new TreeSet<E>());
          ...
         synchronized (set) {
           // Must be in the synchronized block
           Iterator<E> it = set.iterator();
           while (it.hasNext()){
             foo(it.next());
           }
         }

  or:

         NavigableSet<E> set = synchronizedNavigableSet(new TreeSet<E>());
         NavigableSet<E> set2 = set.descendingSet().headSet(foo);
          ...
         synchronized (set) { // Note: set, not set2!!!
           // Must be in the synchronized block
           Iterator<E> it = set2.descendingIterator();
           while (it.hasNext())
             foo(it.next());
           }
         }

  Failure to follow this advice may result in non-deterministic behavior.

  The returned navigable set will be serializable if the specified navigable set is serializable.

  Parameters:
    `navigableSet` - the navigable set to be "wrapped" in a synchronized navigable set.
  Returns:
    a synchronized view of the specified navigable set.
  Since:
    13.0

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