Question

Given the expression A ∩ (B − C), can you use the distributive law to say:

A ∩ (B − C) = (A ∩ B) – (B ∩ C)

Why or why not?

Answer 1

Explanation:

We know that X-Y = X∩Y'

Using it ,we get

A ∩(B∩C') which can be written as (A∩B)∩C' or (A∩B) - C

And right hand side is

(A∩B)-(B∩C) =B ∩(A-C) = B∩(A∩C') = A∩B∩C'

Since both left and right side both leads to same expression A∩B∩C'

Therefore both are equal.