1. (S -> Q) * (Q -> ~S)
2. S v Q
3. ~Q /P * R
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4. S 2, 3 DS
5. S -> Q 1 Simp.
6. Q 5, 4 MP
7. Q * ~Q 6, 3 Conj.
8. F 7 Contradiction
9. F v P 8 Add.
10. P 10 See note below
11. F v R 8 Add.
12. R 11 See note below
13. P * R 10,12 Conj.
Note: p v q is true when either p or q is true. Put another way, p v q is only false when both are false. So for something like F v p (where F stands for false), the truth value of F v p depends entirely on p. So this means that F v p is logically equivalent to p (ie they have the same truth values). Therefore, F v P is equivalent to P, and F v R is equivalent to R.