Simplify each of the following 2 expressions AC B DF A C

Simplify each of the following 2 expressions. (A\'C + B\' + DF) [A +C\' + B\' + DF\'] (AC + B\') (G + F + DE) (AC + B\')\'

Solution

5.1

(A\'C+B\'+DF\')[A+C\'+B\'+DF\']

=(A\'C+B\'+DF\')(A\'C+B\'+DF\')[SINCE DEMORGAN LAW (A . B )\'= A\' + B\')

HENCE FROM THE ABOVE EXPRESSION

(A\')\'+C\'=A\'C (SINCE FROM DEMORGANS LAW)

HENCE

=(A\'C +B\'+DF\')(A\'C+B\'+DF\')[SINCE A.A=A FROM BOOLEAN ALZEBRA]

=(A\'C+B\'+DF\')(THIS IS THE FINAL SOLUTION)

5.2 (AC+B\')(G+F+DE)(AC+B\')\'

ACCORDING TO BOOLEAN ALGEBRA

A.A\'=0

0.A=0

A.B=B.A

A.(B.C)=(A.B).C

from above to the expression

(AC+B\')(G+F+DE)(AC+B\') -1

FROM ABOVE A.B=B.A(I.E FROM BOOLENA ALZEBRA)

SIMLARLY TO THE EXPRESSION

(AC+B\')(G+F+DE)=(G+F+DE)(AC+B\') -1

SUBSTITUE ABOVE TO THE EXPRESSION -1

(G+F+DE).(AC+B\').(AC+B\')\'=(G+F+DE).0(SINCE A.A\'=0 FROM BOOLEAN ALGEBRA)

=O.(G+F+DE)(SINCE A.B=B.A FROM BOOLEAN ALZEBRA)

=0(SINCE O.A=0 FROM BOOLEAN ALZEBRA)

=0