For all sets A and B, A – (A ∩ B) = A – B

Solution:

According to the question,

There are two sets A and B

To prove: A – (A ∩ B) = A – B

L.H.S = A – (A ∩ B)

Since, A – B = A ∩ B’, we get,

= A ∩ (A ∩ B)’

= A ∩ (A ∩ B’)’

Since, (A ∩ B)’ = A’ ∪ B’, we get,

= A ∩ (A’ ∪ B’)

Since, Distributive property of set ⇒ (A ∩ B) ∪ (A ∩ C) = A ∩ (B ∪ C), we get,

= (A ∩ A’) ∪ (A ∩ B’)

Since, A ∩ A’ = Φ, we get,

= Φ ∪ (A ∩ B’)

= A ∩ B’

Since, A – B = A ∩ B’, we get,

= A – B

= R.H.S

Hence Proved