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Math Help - convert statement to logical connectives

  1. #1
    Newbie
    Joined
    Sep 2008
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    Question convert statement to logical connectives

    pls help me with this problem

    let p ,q, r denote the following atomic statements

    p:today is monday
    q:the grass is wet
    r: the dish ran away with the spoon

    write the following in terms of p,q,r and logical connectives

    1.Today is monday and the dish did not run away with the spoon

    2.Either the grass is wet or today is monday.

    3.Today is not monday and the grass is dry

    4.The dish ran away with the spoon, but the grass is wet

    I thank anybody who answers this post in advance
    By the way sorry for posting 2 threads consecutively.
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  2. #2
    Super Member

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    Lexington, MA (USA)
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    Hello, zerodigit!

    p\!:\;\text{Today is Monday}
    q\!:\;\text{The grass is wet}
    r\!:\;\text{The dish ran away with the spoon}

    Write the following in terms of p,q,r and logical connectives


    1)\;\;\underbrace{\text{Today is Monday}}_{p}\; \underbrace{\text{and}}_{\wedge}\; \underbrace{\text{the dish did not run away with the spoon}}_{\sim r} \qquad p \;\wedge \sim r




    2)\;\text{Either }\underbrace{\text{the grass is wet}}_{q}\:\underbrace{\text{or}}_{\vee}\:\underbr  ace{\text{today is Monday}}_{p} \qquad q \vee p




    3)\; \underbrace{\text{Today is not Monday}}_{\sim p}\:\underbrace{\text{and}}_{\wedge}\:\underbrace{  \text{the grass is dry}}_{\sim q} \qquad \sim p \;\wedge \sim q




    4)\; \underbrace{\text{The dish ran away with the spoon}}_{r}\: \underbrace{\text{but}}_{\wedge}\: \underbrace{\text{the grass is wet}}_{q} \qquad r \wedge q


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