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.

dont understand

step-by-step explanation: