Q. 125.0( 1 Vote )

Prove that A ∩ (A B)’ = ϕ

LHS = A (A B)’

Using De-Morgan’s law (A B)’ = (A’ B’)

LHS = A (A’ B’)

LHS = (A A’) (A B’)

We know that A A’ = ϕ

LHS = ϕ (A B’)

We know that intersection of null set with any set is null set only

Let (A B’) be any set X hence

LHS = ϕ X

LHS = ϕ

LHS = RHS

Hence proved

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