Question: Using quantifiers, give a formal expression for the following statement:
"The natural number p is prime"
Thanks all
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:
$\displaystyle F(p)$: $\displaystyle p\in\mathbb{N}\wedge\forall k(k\in\mathbb{N}\Rightarrow(\exists n(n\in\mathbb{N}\wedge n\times k=p)\Rightarrow (k=1\vee k=p)))$