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?

Step-by-step 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.