Hello rebbeca,

I will help you with the first one. Reflexivity in this case means . Since and are subsets of , they need not to be equal to . This leads us to the idea that we may construct an counterexample to the statement of reflexivity.

Let , and . Then and , thus . If we now take an arbitrary element of , say , we see that is not an element of . This is a rather extreme example, since also and are not elements of the relation .

Symmetry in this case means . Thus we start by letting be arbitrary elements of and assume . By the definition of union this means or . Thus we have to consider two cases.

1. case:

This means and , thus . We have therefore .

I hope my post helps you, so that you are able to do the second case on your own and to solve the problem.

Best wishes,

Seppel