Question

if AcB, provd that AnCcBnc​

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).

Reference https://www.physicsforums.com/threads/proof-of-a-bnc-a-b-u-a-c.697377/