1.

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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