Using the Boolean algebra laws and identities prove the foll

Using the Boolean algebra laws and identities, prove the following expression: (A + B) middot (A + C) = A + (B middot C) and mention the laws used in each step of the simplification.

Solution

Ans)

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

(A + B).(A + C)=
	A.A + A.C + A.B + B.C	– Distributive law
	A + A.C + A.B + B.C	– Idempotent AND law (A.A = A)
	A(1 + C) + A.B + B.C	– Distributive law
	A.1 + A.B + B.C	– Identity OR law (1 + C = 1)
	A(1 + B) + B.C	– Distributive law
	A.1 + B.C	– Identity OR law (1 + B = 1)
	A + (B.C)	– Identity AND law (A.1 = A)