Prove that A – (B U C) = (A – B) ∩ (A – C)

Question: Prove that A – (B U C) = (A – B) ∩ (A – C)

Answer:  Let’s analyze step by step

A−(B∩C)

A∩(B∪C)c

A∩Bc∩Cc

A∩A∩Bc∩Cc

A∩Bc∩A∩Cc

(A∩Bc)∩(A∩Cc)

(A−B)∩(A−C)