Absorption's Law - Negative proposition affects the law?

Question

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?

Answer 1

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.