Simplify the Boolean expression F = C(B + C)(A + B + C).
Ans. Simplification of the given Boolean Expression F = C (B +C) (A+B+C) given as
F = C (B+C) (A+B+C)
= CB + CC [(A+B+C)]
= CB + C [(A+B+C)] (Q CC = C)
= CBA + CBB + CBC + CA + CB + CC
= ABC + CB + CB + CA + CB + CC (Q CBB =CB & CBC = CB)
= ABC + CB + CA + C (Q CB+CB+CB = CB; CC = C)
= ABC + BC + C (1+A)
= ABC + BC + C (Q 1+A = 1)
= ABC + C (1+B)
= ABC + C (Q 1+B = 1)
= C (1+AB) = C {Q (1+AB)=1}