Slowly being introduced to Propositional Logic…did I do this right?

Question

I want to make sure I'm getting the concept down. The question is asking

(P'-->Q') [AND] Q [AND] (P-->R) --> R

Here is what I did:

1. (P'-->Q') = (Hypothesis)

2. Q = (Hypothesis)

3. (P-->R) = (Hypothesis)

4. P = (1,2, modus tollens)

5. R = (3,4, modus ponens)

Is that correct? What I'm struggling to understand is which statement I should prove first and how I know if I'm including enough steps and all that and I just wanted to see if I got a good grasp of this concept. I will obviously do more examples but I just want to see if I'm headed in the right direction.

Answer 1

Yes.   That is okay.

$$\begin{align}&\begin{array}{rll} 1. & (P'\to Q') & \text{(Hypothesis)} \\ 2. & Q &\text{ (Hypothesis)} \\ 3. & (P\to R) &\text{ (Hypothesis)} \\ 4. & P &\text{ (1,2, modus tollens)} \\ 5. & R &\text{ (3,4, modus ponens)} \end{array} \\[2ex] \therefore\quad & (P'\to Q') , Q , (P\to R) \vdash R\end{align}$$

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