How to Solve The Redundant Literal Rule (OR)?

Question

I found on the internet this rule (A + B = A + A̅ B) and its called Redundant Literal Rule. this is it's OR form. But I want to know is this really form of the Redundant Literal Rule?. I saw in a website there are 2 Types in this Law. What do you think about that. Is that true? (proves can add as comments)

Answer 1

We have that $$A + A'B = A (1) + A'B = A (1 + B) + A'B $$ $$= A + AB + A'B = A + B (A + A')$$ $$= A+B (1) = A + B $$ where $A'$ is the complement of $A $. Hope it helps.

Answer 2

A + A̅B

= (A + AB) + A̅B (Rule : A = A + AB)

= A + (AB + A̅B)

Taking B common,

= A + B (A +A̅)

= A + B (Rule : A + A̅ = 1)