Simplify the expression abacdadbcab I just need a walk throu

Simplify the expression ab’(a’cd+(ad+b’c’)’)(a’+b) I just need a walk through the problem with the properties. Someone already answered this question a while ago but it wasn\'t very clear.

Solution

ab’(a’cd+(ad+b’c’)’)(a’+b)

(ad+b\'c\')\' = (ad)\' (b\'c\')\' Since (A + B)\' = A\' B\'

= (a\' + d\') (b + c) Since (AB)\' = A\' + B\', and (A\')\' = A

= a\'b + a\'c + bd\' cd\'

= ab’(a’cd+a\'b + a\'c + bd\' cd\')(a’+b)

= ab\'(a\'+b)(a’cd+a\'b + a\'c + bd\' cd\')

= (aa\'b\' + ab\'b)(a’cd+a\'b + a\'c + bd\' cd\')

= 0(a’cd+a\'b + a\'c + bd\' cd\') Since, AA\' = 0(False)

= 0 (False) Since, False . X = False.