How can I further simplify this $A$ + $\neg A B$?

Question

I know there's a rule to simplify this formula $A$ + $\neg A B$, but I am not seeing it. Can someone tell me the name and how to do it?

Answer 1

Assuming that : $A + ¬AB$ is :

$A \lor (\lnot A \land B)$

we have, by Distributivity :

$(A \lor (\lnot A \land B)) \equiv ((A \lor \lnot A) \land (A \lor B)) \equiv (TRUE \land (A \lor B)) \equiv (A \lor B)$

by Identity laws : $TRUE \land p \equiv p$.

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If instead the formula is : $(A \lor \lnot A) \land B$, we have simply : $TRUE \land B \equiv B$.