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Math Help - A logic question

  1. #1
    Junior Member Researcher's Avatar
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    Sep 2009
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    Lightbulb A logic question

    Hello all.
    Is the following expression true?
    [ ( p \equiv q ) \wedge ( r \equiv s ) ] \Rightarrow [(  p \wedge r ) \equiv  ( q \wedge s )]
    If yes, please prove it.

    Thanks
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  2. #2
    MHF Contributor
    Grandad's Avatar
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    South Coast of England
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    Proof by Truth Table

    Hello Researcher
    Quote Originally Posted by Researcher View Post
    Hello all.
    Is the following expression true?
    [ ( p \equiv q ) \wedge ( r \equiv s ) ] \Rightarrow [(  p \wedge r ) \equiv  ( q \wedge s )]
    If yes, please prove it.

    Thanks
    Yes - see the attached truth table for the proof.

    The columns are evaluated in order from (1) to (7) - column (7) being the final result, which shows TRUE on every line.

    Grandad
    Attached Thumbnails Attached Thumbnails A logic question-untitled.jpg  
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  3. #3
    Junior Member Researcher's Avatar
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    Thank you Grandad.
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