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Thread: tautologies without truth table.

  1. #1
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    tautologies without truth table.

    The question is : show that the following propositions are tautologies without using truth table.
    (p∨~q)∧(~p∨~q)∨q

    Can anyone help me? Is it correct what i am doing?
    tautologies without truth table.-27048778_1892524590781267_380242105_o.jpg
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  2. #2
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    Re: tautologies without truth table.

    Quote Originally Posted by jayjdd2 View Post
    The question is : show that the following propositions are tautologies without using truth table. (p∨~q)∧(~p∨~q)[COLOR=#242729][FONT=MathJax_Main]∨q
    I find your notation confusing. Using a standard order of operation here is my take.
    $\begin{gathered}
    \left\{ {(p \vee \neg q) \wedge (\neg p \vee \neg q)} \right\} \vee q &\equiv \left\{ {(p \wedge \neg p) \vee \neg q} \right\} \vee q \\
    &\equiv \left\{ {(F) \vee \neg q} \right\} \vee q \\
    &\equiv \left\{ {\neg q} \right\} \vee q \\
    &\equiv T \\
    \end{gathered} $
    Last edited by Plato; Jan 21st 2018 at 06:09 PM.
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  3. #3
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    Re: tautologies without truth table.

    Thanks! I understand it.
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