For any finite sets A and B, A is related to B if A is a subset of B. For any finite sets A and B, A is related to B if A intersect B is empty.

Question

Which of the following relations are symmetric? Select all that apply.

Group of answer choices

For a function f: A --> B: xRy iff f(x)=f(y)

For any finite sets A and B, A is related to B if A is a subset of B.

For any finite sets A and B, A is related to B if A intersect B is empty.

Answer 1

f(x)=f(y)⇒x=y (symmetrical), so xRy=yRx.

A is related to B if A⊆B (A is a subset of B), A⋂B=A (intersection of A with B must be A). However, B is not a subset of A unless A=B (so A⊆B⇏B⊆A, which is not symmetrical). But B⋂A=A⋂B=A (this relationship is symmetrical).

If A⋂B={} then there are no common elements between A and B so A cannot be a subset of B, so A is not related to B: A⊈B. And B⊈A (symmetrical). That is, A is not related to B, nor is B related to A. This non-relation is symmetrical! However, if there is no relation between the sets, there is nothing to constitute symmetry, so we would have to say the "relationship" is not symmetrical.