How can I prove that A or ((not A) and B) is equivalent to A or B?

Question

I tried AND'ing the leftmost A with itself to keep the expression balanced, but then I wasn't able to put A and (not A) in evidence. I was also trying to apply De Morgan's Theorem, but I cannot AND the leftmost A with (not B).

The simplest way is to show that both expressions have the same truth table. — Karl, Mar 15 '22 at 06:10

score 2 · Accepted Answer · answered Mar 15 '22 at 06:16

2

$$A+(\overline A\cdot B)\\≡(A+\overline A)\cdot(A+B)\\≡1\cdot(A+B)\\≡(A+B)\cdot1\\≡A+B$$

The laws applied, in order:
distributive law
complement law
commutative law
identity law.

answered Mar 15 '22 at 06:16

ryang

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How can I prove that A or ((not A) and B) is equivalent to A or B?

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