QUESTION: Using Boolean rules and laws ,simplify the following expressions. 1. AB + ABC + ABC = A(..

QUESTION: Using Boolean rules and laws ,simplify the following expressions.

1. AB + ABC + ABC = A( B+C ).

AB + ABC + ABC = A( B+C ).

LHS A( B + BC +BC ) …………………………distributive law

A( B + C( B + B) ) ……………From summation rulesB + B =1

Thus the equation simplifies to …

A( B + C).

2. AB + AC +ABC( AB+ C) = 1

 

AB + AC +ABC( AB+ C) = 1

LHS AB + AC + ABCAB + ABCC ……………..distributive law.

SinceA * A = A and B * B = 0…. ………from product rules

Thus the equation simplifies to…AB + AC + A B C.

=A( B + BC ) + AC …………….. distributive law.

But B + BC = B + C ………absorption rule.

Thus the equation simplifies to….A( B + C ) + AC

= AB + AC + AC …………….. distributive law.

AC + AC = 1 ………………….from summation rule

Thus we have ….AB + 1.

AB + 1 = 1………….. from summation rule.