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

"The natural number p is prime"

Thanks all :)

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- Feb 11th 2009, 07:52 AMukroboThe natural number p is prime
Question: Using quantifiers, give a formal expression for the following statement:

"The natural number p is prime"

Thanks all :) - Feb 11th 2009, 08:16 AMclic-clac
A prime $\displaystyle p$ is a natural number whose unique positive divisors are $\displaystyle 1$ and $\displaystyle p.$

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

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

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

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