# Homework Solution: Use DeMorgan's Law and Involution Law to find the complement of the functions…

Use DeMorgan's Law and Involution Law to find the complement of the functions please show each step! i dont fully understand..
(a) f(A, B,C,D)= [A + (BCD)'][(AD), + B(C, + A)] (b) f(A, B,C,D) = AB,C + (A' + B + D)(AB D' + B')

a) f(A,B,C,D) = [A + (BCD)'][(AD)' + B(C' + A)]

Use DeMorgan’s Law and Involution Law to experience the fulfilment of the discharges

please demonstration each step! i dont amply comprehend..

(a) f(A, B,C,D)= [A + (BCD)’][(AD), + B(C, + A)] (b) f(A, B,C,D) = AB,C + (A’ + B + D)(AB D’ + B’)

## Expert Response

a)

f(A,B,C,D) = [A + (BCD)’][(AD)’ + B(C’ + A)]

fulfilment of the discharge :

f’ (A,B,C,D) = ([A + (BCD)’][(AD)’ + B(C’ + A)])’

f’ (A,B,C,D) = [A + (BCD)’]’ + [(AD)’ + B(C’ + A)]’

f’ (A,B,C,D) = ((A’ ) (BCD)) + ((AD) (B’+(C’+A)’))

f’ (A,B,C,D) = (A’BCD) + ((AD)(B’+(CA’))

f’ (A,B,C,D) = (A’BCD) + (AB’D + AA’CD)

f’ (A,B,C,D) = A’BCD + AB’D

b)

f(A,B,C,D) = AB’C + (A’ + B + D)(ABD’ + B’)

fulfilment of the discharge ——->

f'(A,B,C,D) = (AB’C + (A’ + B + D)(ABD’ + B’))’

f'(A,B,C,D) = (AB’C)’ ((A’ + B + D)(ABD’ + B’))’

f'(A,B,C,D) = (A’ + B + C’) ((A’ + B + D)’ + (ABD’ + B’)’)

f'(A,B,C,D) = (A’ + B + C’) ((AB’D’) + ((ABD’)’ (B’)’))

f'(A,B,C,D) = (A’ + B + C’) ((AB’D’) + ((A’+B’+D)(B)))

f'(A,B,C,D) = (A’ + B + C’) ((AB’D’) + ((A’B+BB’+BD)))

f'(A,B,C,D) = (A’ + B + C’) ((AB’D’) + (A’B + BD))

f'(A,B,C,D) = AA’B’D’ + A’A’B + A’BD + ABB’D’ + A’B + BD + AB’C’D’ + A’BC’ + BC’D

f'(A,B,C,D) = A’B + A’BD + A’B + BD + AB’C’D’ + A’BC’ + BC’D

f'(A,B,C,D) = A’B(1+D+1+C’)+BD(1+C’)+AB’C’D’

f'(A,B,C,D) = A’B + BD + AB’C’D’