Q. 2 D4.7( 11 Votes )

# For any two sets A and B, prove the following:

A – B = A Δ (A ∩ B)

Answer :

= A Δ (A ∩ B) [∵ E Δ F =(E–F) ∪ (F–E) ]

= (A–( A ∩ B)) ∪ (A ∩B –A) [∵ E – F = E ∩ F’]

= (A ∩ (A ∩ B)’) ∪ (A∩B∩A’)

= (A ∩ (A’∪B’)) ∪ (A∩A’∩B)

= ϕ ∪ (A ∩ B’) ∪ ϕ

= A ∩ B’ [∵A ∩ B’ = A–B]

= A–B

=LHS

∴ LHS=RHS Proved.

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