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I am currently in a Discrete Math class and reviewing some of my terminology and I don't really understand the Absorption Law. I am not looking for a proof or a truth table but an explanation in layman's terms.

Absorption Law $$ A ∨ (A ∧ B) = A $$ $$ A ∧ (A ∨ B) = A $$

$$ A ∪ (A ∩ B) = A $$ $$ A ∩ (A ∪ B) = A $$

dfeuer
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NightMarcher
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  • Are you trying to understand what they mean, why they are true, why they matter, or something else? These would all be valid questions, and it's not clear to me which you are asking. – dfeuer Oct 22 '13 at 20:10
  • I don't understand what happens to "B". In the first example its seems that the "A" becomes dominant and wipes out the "B" is that why it equals "A"? – NightMarcher Oct 22 '13 at 20:13
  • I understand that A is true OR (A AND B) are true...why is it that B cannot be true? – NightMarcher Oct 22 '13 at 20:19
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    $B$ can be true. Its value just doesn't affect the value of the whole expression. Suppose $A$ is true. Then $A\lor\underline\quad$ is true however you fill in the blank. If $A$ is false, then $A\land\underline\quad$ is false however you fill in the blank. – dfeuer Oct 22 '13 at 20:24

3 Answers3

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For the first one, either $A$ is true, or both $A$ AND $B$ are true. In either case, $A$ is true. On the other hand, if $A$ is true, then the first is true so the expression is true.

The others are similar.

vadim123
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$A\vee (A\wedge B) \\ = (A\wedge T) \vee (A \wedge B) \\= A \wedge (T \vee B) \\= A \wedge T \\= A$

Note : in the third line i used the inverse of distributive law

SmartCoder
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As per logic perspective, we think values either as TRUE or FALSE, I.e: 0 or 1.

So here we can assume 0 or 1 only, for A and B respectively.

So consider A=1 and B=0, Now put the values in asking law, LHS=A.(A+B) =1.(1+0) =1.(1) =1=A ...[because A=1] =RHS

Now you are thinking, why I cannot take value of B=1 and A=0, Yes!! You are independent to that, If you take A=0 then multiply with adjacent terms in bracket, your whole answer will be zero, again, lhs will be equal to rhs. So you will get answer as the value of A in every attempt.

Now for A+(A.B)=A If A=1, B=0

Put, 1+(1.0)=1 [A=1]

Or if A=0, B=1 Then, A+(A.B)=A 0+(0.1)=0 [A=0]

Hence you will get answer as A alwasy!!!!

Ubaid Siddiqui
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