A+(NOT A)B=A+B

How do you get A+B as the answer

To understand how to get A+B as the answer to the equation A + (NOT A)B = A + B, let's break it down step by step:

1. Distributive Property: In the given equation, you have (NOT A)B. By applying the distributive property, you can multiply (NOT A) with each term inside the parentheses.

(NOT A)B = (NOT A)(B) = (NOT A)*B

2. De Morgan's Laws: The term (NOT A) means the complement or inverse of A. According to De Morgan's Laws, the complement of a logical expression can be obtained by negating each term and changing the operator.

(NOT A)*B = (A')*B

(NOT A) is equivalent to A' (pronounced as "A prime" or "NOT A").

3. Boolean Identity Law: According to the Boolean Identity Law, A + A' = 1, where 1 represents true or a logic high. In other words, the sum of a term and its complement is always equal to true.

Therefore, A + A' = 1.

4. Simplification: By substituting A + A' with 1 in the given equation and applying the Boolean Identity Law, you get:

A + A'*B = A + B

Since A + A' equals 1, it can be replaced with the constant 1 in any logical expression without changing its value.

Thus, A + B is the simplified form of the equation A + (NOT A)B = A + B.