I'm in an Intro to Abstract Mathematics class, and I have this proof on my homework. I'm not really sure how to do this one.
I know that X x Y consists of a set of cartesian pairs with values (a,b), where a is an element in X and b is an element in Y. X x Z consists of a set of cartesian pairs with values (a,c), where c is an element of Z. If we assume Y=Z to not be true, there must be a value of b that is not in Z. This would mean that there is a pair (a,b) where there is no value c that equals b. Therefore, X x Y could not equal X x Z if Y didn't equal Z.
That's as close as I've gotten, but it feels wordy and like I haven't really proved anything. I've basically just said "they are equal because they are". Can anyone help?