Question

prove that a minus b intersection b is equals to empty set

Answer 1

Step-by-step explanation:

I need to prove the following:

Prove that A∪∅=A and A∩∅=∅

It's my understanding that to prove equality, I must prove that both are subsets of each other. So to prove A∪∅=A, we need to prove that A∪∅⊆A and A⊆A∪∅.

However, I found an example proof for A∪A in my book and I adapted it and got this:

A∪∅= {x:x∈A or x∈∅} = {x:x∈A} = A

A∩∅= {x:x∈A and x∈∅} = {x:x∈∅} = ∅