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Math Help - Need to check this work

  1. #1
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    Need to check this work

    Hi

    I am trying to answer the question which I have attached. Please tell me if the answers are correct.

    a) let M(x,y) = x has forgiven y R(x)= x is a saint

    U=universe of discourse= all humans

    \forall x \left[\exists y M(x,y)\Rightarrow R(x) \right]

    b)let R(x) = x is in calculus class ; Q(x) = x is in discrete math class
    M(x,y)= x is smarter than y
    U=universe of discourse = all humans

    \forall x \left[R(x)\Rightarrow \neg\left(\forall y\left[Q(y)\RightarrowM(x,y)\right]\right)\right]

    c)let P(x) = x likes mary ; R(x) = x is mary
    U=universe= all humans

    \left[\forall x \left(\neg R(x)\Rightarrow P(x)\right)\right]\wedge\left[\forall x\left( R(x)\Rightarrow \neg P(x)\right)\right]

    d)let P(x) = x is a police officer
    Q(x) = x is jane
    R(x)= x is roger
    M(x,y) = x saw y
    U=universe= all humans

    \forall x \left[ Q(x)\Rightarrow \exists y\left ( P(y)\wedge M(x,y) \right)\right]\wedge \forall x \left[ R(x)\Rightarrow \exists y \left( P(y) \wedge M(x,y) \right ) \right]

    e)let P(x) = x is police officer
    M(x,y) = x saw y
    let j=jane and r=roger
    again U=universe of discourse = all humans

    \exists y \left( P(y)\wedge M(j,y)\wedge M(r,y) \right)

    thanks
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  2. #2
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    Re: Need to check this work

    can anybody help ?

    thanks
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  3. #3
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    Re: Need to check this work

    I think this is correct. (In (b), you need to insert a space between \Rightarrow and M.)

    I am not sure if your problem allowed defining individual constants along with predicates. In (e) you did define j and r. For example, (c) could be ∀x (L(x,m) <-> x ≠ m) where L(x,y) means x likes y and m means Mary.

    It is easier to read formulas if predicates are named mnemonically, e.g., C(x) for calculus, S(x,y) for saw, etc.
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  4. #4
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    Re: Need to check this work

    thanks makarov

    so b) will be

    \forall x \left[R(x)\Rightarrow \neg\left(\forall y\left[Q(y)\Rightarrow M(x,y)\right]\right)\right]

    c) becomes much simpler with your approach, thanks
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