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Math Help - The natural number p is prime

  1. #1
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    The natural number p is prime

    Question: Using quantifiers, give a formal expression for the following statement:

    "The natural number p is prime"


    Thanks all
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  2. #2
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    A prime p is a natural number whose unique positive divisors are 1 and p.

    So we can write for F(p): "the natural number p is a prime"

    F(p): p\in\mathbb{N}\wedge\forall k(k\in\mathbb{N}\Rightarrow(k|p\Rightarrow (k=1\vee k=p)))

    What you call formal may depend on what symbols you can use. If only a symbol \times for multiplication is allowed (and the division one | isn't), it becomes:

    F(p): p\in\mathbb{N}\wedge\forall k(k\in\mathbb{N}\Rightarrow(\exists n(n\in\mathbb{N}\wedge n\times k=p)\Rightarrow (k=1\vee k=p)))
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