Propositional Logic simplification

Question

I was wondering if anyone could help me to understand how this is simplified:

P v (P ^ Q)

The answer is:
1) (P ^ T) v (P v Q) - apply Identity.
2) P ^ (T v Q) - apply Distributive.
3) (P ^ T) - apply Identity.
4) P - apply identity.

Steps 3, and 4 I get.

I don't see how step 1 is an application of Identity.
Identity states: P v T = T... P v F = P... P ^ T = P... P ^ F = F...

So from: P v (P ^ Q)

How is step 1 applying identity? I can't seem to understand how that uses identity.

Thanks.

Answer 1

Step one is taking $P$ and expressing it as $P\land T$ which as one of your identities states, is equivalent to $P$.

So $$\color{blue}{\bf P} \lor (P\land Q) \equiv \color{blue}{\bf (P \land T)} \lor (P\land Q)$$