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Question

For any two sets A and B, A-BB-A=
(a) A-BA
(b) B-AB
(c) AB-AB
(d) ABAB.

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Solution

(c) AB-AB

A-BB-A = AB'BA'=ABA'B'BA' Using distribution law=ABAA'B'BB'A' Using distribution law=ABUUB'A' AA'=U=B'B =ABB'A' ABU=AB and UB'A'=B'A' =AB AB' AB'=B'A'=AB AB-AB=AB-AB

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