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.

step-by-step explanation:

we are given

since, we have to isolate x on anyone side

so, we can move all x terms on one side

subtract both sides by 2x

add both sides by 9

divide both sides by 4

we get

(3x-8) or (3x+8)

step-by-step explanation: