1.

For any two sets A and B, (A − B)⋃(B − A) =A. (A - B) ⋃ AB. (B - A) ⋃ BC. (A ⋃ B) - (A ⋂ B)D.(A ⋃ B) ⋂ (A ⋂ B)

Answer»

(A∖B)⋃(B∖A)=[A⋂B' ]⋃[B⋂A'] 

= [A⋃(B⋂A' )]⋂[B'⋃(B⋂A' )] 

= [(A⋂B)⋃(A⋂A' )]⋂[(B'⋂B)⋃(B'⋂A' )] 

= [(A⋂B)⋃ϕ]⋂[ϕ⋃(B'⋂A' )] 

= [(A⋂B)]⋂[(B'⋂A' ) 

= [(A⋂B)]⋂[(B⋃A)' ] 

= (B⋃A)'⋂(A⋂B) 

=(A⋃B)∖(A⋂B)



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