Prove that A - (B U C) = (A - B) ∩ (A - C) - Maths - Sets

Question

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

Rambaboo Khatana · Accepted Answer

Dear Student,

Let x∈A - B∪C⇒x∈A and x∉B∪C⇒x∈A and x∉B and  x∉C⇒x∈A and x∉B and  x ∈A and x∉C⇒x∈A-B and  x∈A-C⇒x∈A-B∩A-CSo, A - B∪C ⊆ A-B∩A-C    Similarly, A-B∩A-C ⊆A - B∪CHence, A - B∪C = A-B∩A-C

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