Simplify using DeMorgans theorem a A B C D b AB BC CDSol

Simplify using DeMorgan\'s theorem a) (A + B + C). D b) AB + B(C + CD)

Solution

DEMORGAN\'S THEOREM:

(AB)\'=A\'+B\'

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

(i)

((A+B+C).D)\'
(A+B+C)\'+D\'
(A\'.B\'.C\')+D\'

=> A\'B\'C\'+D\'

((AB\')+B.(C\'+(CD)\'))\'
(AB\')\'. (B.(C\'+(CD)\'))\'
(A\'B).((B)\'+(C\'+(CD)\')\')
(A\'B).(B\'+((C\')\'.((CD)\')\'))

(A\'B).(B\'+(CCD))

(A\'B)(B\'+CCD)
=> A\'+A\'BCCD