Discussion
The Boolean expression A(A+B) simplifies to
Answer: C
A(A+B) simplifies to A.
Multiply out and use the idempotent and absorption laws:
\[ \begin{aligned} A(A+B) &= AA + AB \\ &= A + AB \\ &= A(1 + B) = A \end{aligned} \]
This is the absorption law. A check with a truth table agrees: when A = 0 the expression is 0, and when A = 1 it is 1 whatever B is. A+B and B depend on B, so they are wrong, and AB is 0 when A = 1 and B = 0, where the expression is 1.
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