Question

A complement B complement + B complement C complement + A complement C complement

Answer 1

Explanation:

(a) (A + B).(B + C).(A + C)

Complement of (A + B).(B + C).(A + C)

= [(A + B).(B + C).(A + C)]'

= (A + B)' + [(B + C).(A + C)]'

= (A + B)' + (B + C)' + (A + C)'

= A'.B' + B'.C' + A'.C'

(b) A.B + (A'.B').(B.C + B'.C')

Complement of A.B + (A'.B').(B.C + B'.C')

= [A.B + (A'.B').(B.C + B'.C')]'

= (A.B)'.[(A'.B').(B.C + B'.C')]'

= (A' + B').[(A'.B')' + (B.C + B'.C')']

= (A' + B').[A + B + [(B.C)' . (B'.C')']]

= (A' + B').[A + B + [(B' + C').(B + C)]]

= (A' + B').[A + B + [BB' + B'C + BC' + CC']]

= (A' + B').[A + B + [0 + B'C + BC' + 0]]

= (A' + B').(A + B + B'C + BC')

= (A' + B').(A + B'C + B(1 + C'))

= (A' + B').(A + B + B'C)

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