Question:
For any three sets A, B and C, (A – B) ∩ (C – B) is equal to ____________.
Solution:
For A, B and C
(A – B) ∩ (C – B) = (A ∩ BC) ∩ (C ∩ BC)
= A ∩ BC ∩ BC ∩ C (∵ intersection is associative)
= A ∩ (BC ∩ BC) ∩ C
= A ∩ BC ∩ C (∵ BC ∩ BC = BC)
= A ∩ C ∩ BC
Hence, (A – B) ∩ (C – B) = (A ∩ C) – B
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