I need some help understanding the steps to take to prove subsets.
For each of the following universal statements regarding any three finite sets $X, Y$, and $Z$, determine whether it is (universally) true or not. If you say it is false (not always true), give a counter-example to show that the statement is not true in that case. If you say the statement is true, provide a proof to show it is true all the time.
My Notes: I can sort of understand the first 3 questions, but I don't understand the multiplication of sets ones. Also note before all these questions, there's (Universal quantifier of $X, Y$, and $Z$)
(solved the first 3 already by myself)
iv. $(X - Y) \times Z \subseteq (X \times Z) - (Y \times Z)$
v. $(X \times Z) - (Y \times Z) \subseteq (X - Y) \times Z$
vi. $(X - Y) \times Z = (X \times Z) - (Y \times Z)$
I really need this help someone urgently, and this is my first time trying this out.