Give a formal two-column proof of the statement, using the statements and rules

Question

Give a formal two-column proof of the statement, using the statements
and rules of inference of Propositional Logic.

((P Q) ^ ¬P ) Q

So far I have:
1)Assume ((P Q) ^ ¬P )
2) (P Q) using (and - )
3) ¬P   using (and - )

I need to get Q from the (P Q) but I'm not sure how.

Here are the 12 rules:

modus ponens) -( Show: W Show : WV Conclude:V Assume W Show: V Conclude: WV Show: WV Show: VW Conclude: W Show : W V Conclude: WV Conclude: VW or + Show: W Conclude: W or V Conclude: V or W or _ (proof by cases) Show: W or V Show : W Show : V Conclude: U not+(proof by contradiction) not-(proof by contradiction) Assume W Show: Assume not W Show: Conclude: not W Conclude: W Show: W Show: not W Conclude: copy Show: W Conclude:W

Explanation / Answer

(P Q) ^ ¬P

= (P ^ ¬P) v (Q ^ ¬P) (Distributive property)

= F v (Q ^ ¬P) (P ^ ¬P is always false)

= Q ^ ¬P (Property of ^)

= Q (Conjunctive simplification).

Another way

(P Q) ^ ¬P

= (¬P -> Q) ^ ¬P (Material implication)

= Q (Modus ponens)

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