Prove (A-B) u (A-C) = A - (BnC)

Question

Mathematics

Morgan Hodges

27 September, 03:00

Prove (A-B) u (A-C) = A - (BnC)

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Casey Hunt · Answer 1

A - (B ⋂ ⋂C) = (A-B) ⋃ ⋃ (A-C) If A-B={xlx ∈ ∈A and x ∉ ∉B} A-C={xlx ∈ ∈A and x ∉ ∉C} then (A-B) ⋃ ⋃ (A-C) = {xlx ∈ ∈A, x ∉ ∉ (B and C) Let X=A and Y = (B ⋂ ⋂C) X-Y={xlx ∈ ∈X and x ∉ ∉Y} x ∉ ∉Y x ∉ ∉ (B ⋂ ⋂C) x ∉ ∉ (B and C) Therefore, A - (B ⋂ ⋂C) = (A-B) ⋃ ⋃ (A-C).