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Thread: laws of propositional logic to simplify

  1. #1
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    laws of propositional logic to simplify

    [(p ∨ q) =⇒ r] =⇒ (q ∧ r)

    I got stuck after using implication and demorgan laws.
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  2. #2
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    Re: laws of propositional logic to simplify

    Quote Originally Posted by Dukeham View Post
    [(p ∨ q) =⇒ r] =⇒ (q ∧ r)
    I got stuck after using implication and demorgan laws.
    We do not know the system names you are to use. Therefore you must fill in the justifications.
    $\begin{gathered}
    (p \vee q) \Rightarrow \;r \hfill \\
    \neg (p \vee \;q) \vee \;r \hfill \\
    (\neg p \wedge \neg q) \vee \;r \hfill \\
    (\neg p \vee r) \wedge (\neg q \vee r) \hfill \\
    (\neg q \vee r) \hfill \\
    q \Rightarrow \;r \hfill \\
    \hfill \\
    \end{gathered}$
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