C, D are subsets of A.
How can i determine if these relations:
1)C X D union D X C
2)C X D intersection D X C
are reflexive symmetric or transitive relations?
Thanks for any kind of help
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.
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.