Mark the correct alternative in the following: For any two sets A and B, (A − B) (B − A) =

Question

Philoid · Accepted 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)