State and prove redundant law of boolean algebra.

Question

Statement and proof

Answer 1

Redundancy laws are as follows:

i) A+ĀB = A+B

ii) A.(Ā+B) = AB

Proof:

i) A+ĀB = (A+Ā)(A+B) [since A+BC = (A+B)(A+C){Distributive law}]

            = 1 * (A + B) [since A + Ā = 1{Complement}]

            = A + B

ii) A*(Ā + B) = A.Ā+AB

                   = 0+AB [since AĀ =0{Complement}]

                   = AB

Answer 2

see --

    https://www.nayuki.io/page/boolean-algebra-laws