- #1

zeion

- 466

- 1

## Homework Statement

Hi,

This is a question from a logic course, not sure if I'm doing it right.

Consider the following predicates:

MP(x) : x is a Mersenne prime

Prime(x) : x is Prime

Using the above predicates, provide an equivalent symbolic statement for the statement below:

1) A natural number n is a Mersenne prime if and only if n is a prime number that can be written in the form 2

^{k}- 1 for some positive integer k.

## Homework Equations

## The Attempt at a Solution

[tex] \forall n \in N, MP(x) \Leftrightarrow \exists k \in Z, k > 1 : 2^k - 1= x \wedge Prime (x) [/tex]