boolean algebra

Question

Simplify A + A B (Boolean). Result is:

RankGuru · Accepted Answer

Using the laws of Boolean Algebra:
1. Factor out the common term $A$:
   $A + AB = A \cdot (1 + B)$
2. According to the **Annulment Law** (or Identity Law for OR), $(1 + 	ext{anything}) = 1$:
   $1 + B = 1$
3. Therefore:
   $A \cdot (1) = A$
This is known as the **Absorption Law**. Intuitively, if $A$ is true, the whole expression is true regardless of $B$. If $A$ is false, both terms are false, so the whole expression is false. Thus the result is simply $A$.

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boolean algebra

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