Reflexive, Symmetric, Transitive Relation?

[lookingforhelp]

Let X = {a,b,c} and P(X) be the power set of X. A relation N is defined on P(X) as follows:
For all A, B elements of P(X), A N B <=> the number of elements in A is not equal to the number of elements in B.
Is this relation reflexive, symmetric, transitive, or none, and justify.

I believe that it is symmetric, not reflexive, and not transitive, but I'm not sure how I go about providing a proof for this.
Thank you for the help!

 

[daon2]

Let X = {a,b,c} and P(X) be the power set of X. A relation N is defined on P(X) as follows:
For all A, B elements of P(X), A N B <=> the number of elements in A is not equal to the number of elements in B.
Is this relation reflexive, symmetric, transitive, or none, and justify.

I believe that it is symmetric, not reflexive, and not transitive, but I'm not sure how I go about providing a proof for this.
Thank you for the help!

Yes you are correct

Symmetric and non-reflexive should be obvious i think?

For non-transitive, if A N B, then B N A, is A N A?

 

[lookingforhelp]

Thanks

Thank you for the help!