Boolean expression explanation

Question

Could someone explain how to get the following Boolean expression in its simplest form, I am having difficulties working it out step by step

$$A+B+A*B$$

If you want to visualise what it means, just think of $A \cup B \cup (A \cap B)$. — J.-E. Pin, Mar 29 '16 at 16:01

shardulc · Answer 1 · 2016-03-29T14:49:46.477

2

Note that $A + B + AB = A(B + 1) + B = A + B$ (because $B + 1$ is always 1), so it simplifies to a simple OR function. This can be verified by the truth table as well.

edited Mar 29 '16 at 14:49

answered Mar 29 '16 at 14:44

shardulc

4,562

But only iff $AB=0.$ – Theodoros Mpalis Mar 29 '16 at 14:48
@TheodorosMpalis why only iff $AB = 0$? – shardulc Mar 29 '16 at 14:50
$A+B+AB=A+B\Leftrightarrow AB=0.$ – Theodoros Mpalis Mar 29 '16 at 14:52
@TheodorosMpalis That doesn't seem right. If both $A$ and $B$ are true, then $AB \neq 0$ but $A + B + AB = A + B$ still holds. – shardulc Mar 29 '16 at 14:56
But $AB=0$ indeed, because $B+1=1\Leftrightarrow B=0.$ No ? – Theodoros Mpalis Mar 29 '16 at 15:00
@TheodorosMpalis No. $B + 1 = 1$ regardless of the value of $B$. – shardulc Mar 29 '16 at 15:10

Boolean expression explanation

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