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Thread: Can Anyone Help Me With these Problems

  1. #1
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    Question 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.
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  2. #2
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    Re: Can Anyone Help Me With these Problems

    Quote Originally Posted by marsandfruit View Post
    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
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