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All along I've learned that the Boolean Operator '.' works like AND and '+' works like OR. This pretty much explains most of the laws of Boolean Algebra; they make sense to me. However I don't quite understand the proof of Absorptive Law fully.

X.(X+Y)=X means 'X AND X' OR 'X AND Y', or, X OR X AND Y which is basically X

But when I look at the proof of the Abosrptive Law:

X.(X+Y)=X.X+X.Y=X.1+X.Y=X.(1+Y)=X.1=X

Nothing after the first step makes sense to me. Why should X.X=X.1 and 1+Y=1? You could say these are laws but I don't understand them intuitively. Please help me to.

Rohit Gupta
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Ambica Govind
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    Not "works like AND" but "is AND". AND is the same thing no matter whether you write AND or & or x or . ! – user253751 Aug 24 '22 at 12:28
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    I’m voting to close this question because it's a pure math question and should be asked at the appropriate math site instead. – Lundin Aug 24 '22 at 13:04

1 Answers1

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X AND X is X and is the same as X AND 1 (because that will always take the value of X).

Why is X AND X just X? X can only take 0 or 1. So you have 0 AND 0 = 0 or 1 AND 1 = 1, so the result is exactly your input. And if you look at X AND 1 you get: 0 AND 1 = 0 or 1 AND 1 = 1, again you get out what you put in, so X.1 = X

So that is why: X.X = X = X.1

And 1 OR anything is always 1. You have 1 OR 0, which is 1 and you have 1 OR 1 which is also 1. (it's not an XOR).

So 1+Y = 1.

Arsenal
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