I'm not sure I have these concepts down well enough. The following is a problem from my professor:

Let S = {1,2,3,4,5}. On P(S) define the relation

as follows: A

B iff A

B =

. Is

reflexive? Is

symmetric? Is

transitive?

Since there are elements in P(S) that do not equal

when intersecting themself then

is not reflexive.

If A

B is empty then B

A is empty so

is symmetric.

{1,2}

{3,4} is empty. And {3,4}

{2,5} is empty. But {1,2}

{2,5} = {2}. So

is not transitive.

Is the above correct? If not please explain where I've gone wrong.

Happy KwanzHanukmas!