Question

if A subset b. then b-(b-a) =a​

Answer 1

Answer:

Step-by-step explanation:

We want to show A∪B=BA∪B=B. There are two parts:

First, we want to show B⊆A∪BB⊆A∪B. Assume x∈Bx∈B. Then certainly x∈Ax∈A or x∈Bx∈B, so we are done.

Now we show A∪B⊆BA∪B⊆B. Assume x∈A∪Bx∈A∪B; we want to show x∈Bx∈B. Since x∈A∪Bx∈A∪B, either x∈Ax∈A or x∈Bx∈B. if the latter case holds we are already done. In the former case we can conclude that x∈Bx∈B because of the hypothesis that A⊆BA⊆B.