Discussion
In Boolean algebra, \( A + A \cdot B = A \).
Answer: B
Correct answer: True
The statement is true. This is the absorption law, and it is one of the most useful identities for simplifying expressions. The proof is short: \[ A + A\cdot B = A(1 + B) = A \cdot 1 = A, \] using the distributive law and then the null law \( 1 + B = 1 \), which holds because ORing anything with 1 gives 1. It can also be seen by inspection. If \( A = 1 \) the whole expression is 1 whatever B may be; if \( A = 0 \) then both terms are 0. So the value depends only on A, and B is absorbed. Its dual is \( A \cdot (A + B) = A \), and a related form is \( A + \bar{A}B = A + B \), which is not absorption and is worth keeping distinct. These identities matter because every gate removed from a design saves cost, power and propagation delay - the same purpose served by Karnaugh maps and the Quine–McCluskey method for larger expressions.
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