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Math Help - Boolean Expression

  1. #1
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    Boolean Expression

    How can i Make truth table for the following expression
    ~p→~r V q ~ p V r

    great confusion to start because there is no brackets
    .how can i solve this please help me
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  2. #2
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    Re: Boolean Expression

    Quote Originally Posted by suhail View Post
    How can i Make truth table for the following expression
    ~p→~r V q ~ p V r

    great confusion to start because there is no brackets
    .how can i solve this please help me
    I'm no logic expert but I believe this can be rewritten as

    $(\neg p \rightarrow \neg r) \vee \left(q \wedge (p \vee r)\right)$

    $\neg p$ is the same as $\sim p$ i.e. NOT p
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  3. #3
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    Re: Boolean Expression

    I confirm that $\land$ usually binds stronger than $\lor$. Negation usually binds the stronest, i.e., it pertains only to the smallest following subformula. With respect to $\to$ and $\lor$, conventions may vary. I would parse $A\to B\lor C$ as $A\to (B\lor C)$. In any case, precise rules for parsing formulas should be described in the textbook or lecture notes.
    Thanks from romsek
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  4. #4
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    Re: Boolean Expression

    Quote Originally Posted by romsek View Post
    I'm no logic expert but I believe this can be rewritten as

    $(\neg p \rightarrow \neg r) \vee \left(q \wedge (p \vee r)\right)$

    $\neg p$ is the same as $\sim p$ i.e. NOT p
    Quote Originally Posted by emakarov View Post
    I confirm that $\land$ usually binds stronger than $\lor$. Negation usually binds the stronest, i.e., it pertains only to the smallest following subformula. With respect to $\to$ and $\lor$, conventions may vary. I would parse $A\to B\lor C$ as $A\to (B\lor C)$. In any case, precise rules for parsing formulas should be described in the textbook or lecture notes.
    Yes, you are right. It should be

    $\left(\neg p \rightarrow (\neg r \vee q)\right) \wedge (p \vee r)$
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