Thread: Reflexive, symmetric, and transitive

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!

Originally Posted by oldguynewstudent

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.

Yes, they are all correct.

Originally Posted by oldguynewstudent

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!

You left out "reflexive" but that is easy. Is empty?