Do the domination and identity laws also apply to $\lnot p$?

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I am working on a problem in discrete mathematics and had a quick question.

I know that we have the following relations that define both the identity laws and the domination laws in propositional logic:

Identity Laws:

$p \land T \equiv p$

$p \lor F \equiv p$

Domination Laws:

$p \lor T \equiv T$

$p \land F \equiv F$

My question is do these laws also apply for $\lnot P$?

For example, can we also say that $\lnot P \lor T \equiv T$?

Or does the negation here change any part of the equivalence of this expression?

Any explanations or links to resources would be greatly appreciated.