# Thread: Can Anyone Help Me With these Problems

1. ## Can Anyone Help Me With these Problems

Hello I need help proving these Logic Problems. I've solved most of them but I would like to see what you guys come up with. I am supposed to use the Laws of Sentential Logic and Inference Rules.

Given p, (p → q) and (q → r), prove r.

Given (p ↔ q) and p, prove q.

Given (p∧q) and (p → s), prove s.

Given (¬p → q), ¬q prove p.

Given (p ∨ q) and ¬q prove (p ∨ s).

• Given (p ∨ (q ∧ F)) and (p → q) prove q.

2. ## Re: Can Anyone Help Me With these Problems

Originally Posted by marsandfruit
Hello I need help proving these Logic Problems. I've solved most of them but I would like to see what you guys come up with. I am supposed to use the Laws of Sentential Logic and Inference Rules.

i) Given (p∧q) and (p → s), prove s.

ii) Given (¬p → q), ¬q prove p.

iii) Given (p ∨ q) and ¬q prove (p ∨ s).
i)
1. $p\wedge q$
2. $p\to s$
3. $\therefore s$
4. $p$ 1) simplication
5. $s$ 2)& 4) modus pomens

ii)
1. $\neg p\to q$
2. $\neg q$
3. $\therefore p$
4. $p$ 2) & modus tollens

1. $p\vee q$
2. $\neg q$
3. $\therefore p\wedge s$
4. $p$ 1) & 2) disjunctive syllogism
5. $p\vee s$ 4) & addition