Question 11 - 2 or 3 Mark Questions - Chapter 12 Class 11 - Boolean Algebra

Verify the following using Boolean Laws: A + C = A + A’. C + B.C

Answer:

To prove: A + C = A + A’. C + B.C 

Proof:

RHS

= A + A’. C + B.C 

= (A+A’).(A+C) + B.C                (using distributive law)

= 1.(A+C) + B.C                        (using complement law)

= A + C + (B.C)                         (using identity law)

= A + C.(1+B)                            (using distributive law)

= A + C.1                                   (using annulment law)

= A + C                                      (using identity law)

= LHS

Hence, the expression A + C = A + A’. C + B.C is verified.