If A and B are two given sets, then A ∩ (A∩B)c is equal to
A
B
A ∩ (A∩B)c) = A ∩ (Ac ∪ Bc)
= (A ∩ (Ac ) ∪ (A ∩ (Bc)
= ∅ ∪ (A ∩ (Bc) [∵ (A ∩ (Ac ) = ∅ ]
= A ∩ (Bc)