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Math Help - [SOLVED] Logical Laws and Equivalence

  1. #1
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    [SOLVED] Logical Laws and Equivalence

    Hi,

    Is this the right way to show that (~(p V q) => r) is logically equivalent to (p V q) V r.

    (~(p V q) => r)
    <==> (~~(p V q) V r) Implication Laws.
    <==> (p V q) V r Double Negation.

    Can someone check it for me and prehaps correct me?

    Thanks for help.
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  2. #2
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    Grandad's Avatar
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    Logic Laws

    Hello kurac
    Quote Originally Posted by kurac View Post
    Hi,

    Is this the right way to show that (~(p V q) => r) is logically equivalent to (p V q) V r.

    (~(p V q) => r)
    <==> (~~(p V q) V r) Implication Laws.
    <==> (p V q) V r Double Negation.

    Can someone check it for me and prehaps correct me?

    Thanks for help.
    Provided you can assume that (p \Rightarrow q) \equiv (\neg p \vee q) your proof is fine. An alternative way would be to set up truth tables for \neg(p \vee q) \Rightarrow r and (p\vee q) \vee r and show that they produce the same output.

    Grandad
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  3. #3
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    Yep, i assumed that from one of the Implication laws.

    Thanks Grandad
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