Prove the following statements: s subset s union t t subset s union t s intersection t subset s s intersection t subset t.

proofs:

We want to prove

Let . By definition is the set that contains the elements of and the elements of . Then must be in  . As was arbitrary, we conclude that .

This proof is analogous to the previous one. In fact, this result is the same result as the previous one.

We want to prove

Let . By definition of the intersection should be in and also in . Then, we already saw that . As was arbitrary we can conclude that .

This is the same result as the previous one. There is no need to prove it anymore, but if you wish, you can reply the exact same proof.

b is the answer that makes most sense

step-by-step explanation: