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Simplify the following expression, using Boolean laws: [2] A.(A’ + B).C.(A + B)

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Simplify the following expression, using Boolean laws:

 A.(A’ + B).C.(A + B)

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A.(A’+B).C.(A + B) 

= (AA’ + AB).C.(AA + AB) 

= (0 + AB).C.(A + AB) (∵ AA’ = 0) 

= (AB).C.(A + AB) (∵ A + AB = A) 

= AB.CA 

= AA.BC (∵ A.A = A) 

= A.B.C

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