Boolean Property Simplification

Question

I was wondering if there is a term/property/name to describe this simplification:

$$A + \overline{A}B = A + B$$

thank you

Answer 1

I'll use $\cup$, $\cap$ notation in my proof instead of $+$,$\cdot$, I hope you don't mind (if you aren't familiarized with them, $\cup$ means OR and $\cap$ means AND). Notice that: $$A\cup(\bar A\cap B)=(A\cup \bar A)\cap(A\cup B),$$ and $(A\cup \bar A)$ is the universe, so $$(A\cup\bar A)\cap(A\cup B)=A\cup B,$$ to be said; $$\boxed{A\cup(\bar A\cap B) = A\cup B}$$

Rewriting it using your notation, it goes like this:

$$A+ \bar AB = (A+\bar A)(A+B)=A+B$$