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Math Help - Showing a compuond proposition is a tautology using logical equivalences

  1. #1
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    Showing a compuond proposition is a tautology using logical equivalences

    Hi all,

    I am currently working on showing that [p AND (p IMPLIES q)] IMPLIES q is a tautology and, really just don't know where to begin. Not expecting any answers, but to be pointed in the correct direction.
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  2. #2
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    Re: Showing a compuond proposition is a tautology using logical equivalences

    My first choice would be a truth table but if you must use "logical equivalences" you might start with "A implies B" is equivalent to "not B implies not A". Here that would be "not q implies not (p and (p implies q))"
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  3. #3
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    Re: Showing a compuond proposition is a tautology using logical equivalences

    Thank you. My first choice would have been a truth table but the professor said no specifically to the truth table.
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  4. #4
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    Re: Showing a compuond proposition is a tautology using logical equivalences

    Hello, michaelgg13!

    Darn! Latex isn't working . . .


    Show that: .[p ∧ (p → q)] → q

    I'll list the steps.
    I'll let you supply the reasons.

    We have:

    [p ∧ (~p ∨ q)] → q

    [(p ∧ ~p) ∨ (p ∧ q)] → q

    [F ∨ (p ∧ q)] → q

    (p ∧ q) → q

    ~(p ∧ q) ∨ q

    (~p ∨ ~q) ∨ q

    ~p ∨ (~q ∨ q)

    ~p ∨ T

    . . .T
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