Absorption's Law - Negative proposition affects the law? This is a simple question. It's known that the absorption's law is like the following example: > p ∧ (p V q) = p But, if the proposition has a negation, does this affect the law? for example: > p ∧ **¬(p V q)** = p Is this correct? **Edit:** Is the De Morgan's Law necessary before the Absorption's Law?

De Morgan's Law helps to show that no absorption law holds for your example.

(p ∧ ¬(p V q)) = (p ∧ (¬p ∧ ¬q))

By association we then can get

((p ∧ ¬p) ∧ ¬q)

But, (p ∧ ¬p) is always false, so (p ∧ ¬(p V q)) is always false also.

p can be true or false, and thus no absorption law holds for your example involving negation.