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prove that- AX(B∩C) = (AXB) ∩ (AXC)

Prob. Let A,B,C be any three sets, then prove that-
AX(B∩C) = (AXB) ∩ (AXC)

(x,y) ∈ Ax(B∩C)
x∈A and (y∈(B∩C))
x∈A and (y∈B and y∈C)
(x∈A and y∈B) and (x∈A and y∈C)
(x,y) ∈ (A x B) and (x,y) ∈(A x C) // by Cartesian Product.

(x,y) ∈ (AxB)∩(AxC)

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