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Math Help - rules of inference for quantified statements

  1. #1
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    rules of inference for quantified statements

    ∼(∀x,P(x))

    propositional function "x ≥ x^2

    is true or false


    Could someone tell me if I am correct, if not please explain:

    ∼(∀x,P(x)) = true

    Basically I just prove that (∀x,P(x)) = true and then use the not operator to convert my answer to false.

    Is this a correct way to prove this?
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  2. #2
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    Basically I just prove that (∀x,P(x)) = true
    Please show how you prove this.

    and then use the not operator to convert my answer to false
    So, if you apply negation to both sides of (∀x,P(x)) = true (assuming it is correct), why do you have ∼(∀x,P(x)) = true written above?
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  3. #3
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    I made a mistake: (∀x,P(x)) = false

    when x = 2, then x ≥ x^2 = false

    so I then use the not operator to convert my answer to true which give me the final answer: ∼(∀x,P(x)) = true
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  4. #4
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    could it be better explained this way:

    ∼(∀x,P(x)) = true

    x^2 ≥ x is false when x = 2

    ∃x, ~P(x)

    there exists at least one x that is not true
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  5. #5
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    This seems fine.
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  6. #6
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    OK thanks, I think i have this figured out.
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