# Thread: Help with Proofs - Did I do this correctly?

1. ## Help with Proofs - Did I do this correctly?

(Sorry if is in the wrong topic - I didn't see one for proofs)

I am still trying to get the hang of my proofs class, and I was wondering if I did this problem correctly. The statements above the line are what is given, and below the line are my arguments & reasons that I came up with.

Directions: Derive R

(1) P ^ Q
(2) (P v Q) -> R
-----------------------------
(3) P ..........(1) Simplification
(4) Q ..........(1) Simplification
(5) P v Q .....(3),(4) Addition
(6) R ...........(2),(5) Definition of implication

If I did something wrong, could you please explain what to do? Thanks in advance!

2. You didn't do anything wrong. I'd say you could eliminate line 4 altogether, though. You can introduce line 5 without line 4.

3. Well we turned in the homework yesterday and went over it. Turns out that for the reason for step (6), I should have put Modus Ponens instead of Definition of Implication... Oh well. Now I know for next time.

4. Yeah, I'd agree it was Modus Ponens for the last step. I didn't know exactly what you meant by "definition of implication", so I let it pass. The idea was clearly valid.

5. Yeah, I guess I had forgotten about Modus Ponens when I was doing that problem, so I thought to myself, "Well, if the first part of an implication is proven to be true, then the second part has to be true" and for some reason I just assumed that that was the case because that's how implications are... Oh well, I understand what I did wrong. Thanks again for your help

6. You're very welcome. Have a good one!