Simplify the given expressions using Boolean postulates
Y = (A + B)(A‾ + C)(B + C)
Ans. Y = (A + B)(A‾ + C)(B + C)
= (A A‾ + AC + B A‾ + BC) (B + C)
= (AC + B A‾ + BC) (B + C) (As A A‾ = 0)
= ABC + BB A‾ + BBC + ACC + BA‾C + BCC
= ABC + B A + BC + AC + BA‾C + BC (As BB = B)
= ABC + AC + BA‾ + BA‾C+ BC (As BC + BC = BC)
=AC (B+1) + B A‾ + BC (A‾ +1)
= AC + B A‾ + BC (As B + 1 = 1 and A‾ + 1 = 1)
= AC + B A‾ + BC (A + A‾) (As A + A‾ = 1)
= AC + BA‾ + BCA + BCA‾
= AC(1 + B) + BA‾ (1 + C)
= AC + BA‾ {As (1 + B) = 1 and (1 +C) = 1}.