patternCritical
Why is $A \lor (A \land \neg B) \equiv A$?
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whyequivneglandlor
Problem
I would like to know if there is a rule to prove this. For example, if I use the distributive law I will get only $(A \lor A) \land (A \lor \neg B)$.
Solution
I find pictures are great for anything simple enough to use them, which this is.
Remember:
AND means the area taken up by both things. So the middle one is what is taken up outside B, but also inside A. Their junction is not counted because it is inside A but not outside B.
OR means it is covered by either one or both. Both of them cover the part of A that is outside B, and the junction is covered by A (first picture) so it is counted too.
All in all, you just have A again.
Sorry if this is too simplistic, not sure what level you are at.
Remember:
AND means the area taken up by both things. So the middle one is what is taken up outside B, but also inside A. Their junction is not counted because it is inside A but not outside B.
OR means it is covered by either one or both. Both of them cover the part of A that is outside B, and the junction is covered by A (first picture) so it is counted too.
All in all, you just have A again.
Sorry if this is too simplistic, not sure what level you are at.
Context
StackExchange Computer Science Q#82169, answer score: 55
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