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Math Help - Prove Statement is logically equivalent using laws of logic

  1. #1
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    Question Prove Statement is logically equivalent using laws of logic

    Hello Everyone,

    I just stuck-up while solving the following question:

    Verify this statement is logically equivalent using laws of logic :

    ~(P disjunction q) disjunction (~p ^ q) = ~ p

    Note: here is used word disjunction instead of symbol.

    I need your help and support to solve this problem.
    Thanks.
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  2. #2
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     \sim (p \vee q) \vee \left( { \sim p \wedge q} \right) \equiv \left( { \sim p \wedge  \sim q} \right) \vee \left( { \sim p \wedge q} \right)
    <br />
\left( { \sim p \wedge  \sim q} \right) \vee \left( { \sim p \wedge q} \right) \equiv  \sim p \wedge \underbrace {\left( { \sim q \vee q} \right)}_{true} \equiv  \sim p
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  3. #3
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    Cool Prove statement is true using laws of logic.

    Hello galactus,

    Thanks for Your reply, but if you read my question, i asked to prove this statement using "Laws Of Logic" not by using truth table. I know how to prove it using truth table table.

    Kaleem.
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  4. #4
    Super Member angel.white's Avatar
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    Quote Originally Posted by Kaleem Qureshi View Post
    Hello galactus,

    Thanks for Your reply, but if you read my question, i asked to prove this statement using "Laws Of Logic" not by using truth table. I know how to prove it using truth table table.

    Kaleem.
    I believe Plato already did this for you in post #2 using De Morgan's law, the Distributive law, and the Absorption law.
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