Let T be the set of all movie actors and actresses. For x, y elementof T, define

Question

Let T be the set of all movie actors and actresses. For x, y elementof T, define x R y if there is some movie that both x and y appear in. Which properties of equivalence relations does R satisfy? The relation reflexive, because every actor/actress in a movie with The relation symmetric, because if a has been in a movie with b then b in a movie with The relation transitive, because a could appear with b in a movie, b could appear in another movie with c, and that guarantee that a will appear in a movie with

Explanation / Answer

In mathematics, an equivalence relation is a binary relation that is at the same time a reflexive relation, a symmetric relation and atransitive relation. As a consequence of these properties an equivalence relation provides a partition of a set into equivalence classes

1.the relation is reflexive because every actor work in a movie with X,Y

2.the relation is symmetric if a has been in a movie with b ,then b has been in a movie with a

3.the relation is transitive ................and that B guarantee that a will appear in a movie with C

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