Let A and B be sets. If A∩X=B∩X=ϕ and A∪X=B∪X for some set X, show that A=B. (Hints A=A ∩(A ∪ X),...

Let A and B be sets. If A∩X=B∩X=ϕ and A∪X=B∪X for some set X, show that A=B.
(Hints A=A ∩(A ∪ X), B=B ∩(B ∪ X) and use Distributive law )
Given: A ∩ X=B ∩ X=φ
A ∪ X=B U X for some set X
TST: A=B
Pf: A=A ∩(A ∪ X)
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