Predicate logic/Arithmetical predicates/Formulate/3/Exercise

Formulate the following unary predicates within the natural numbers ${}\mathbb {N} =\{0,1,2,3,\ldots \}$, only using equality, addition, multiplication and logical connectives and quantifiers.

1. ${}x$ is a multiple of ${}10$.
2. ${}x$ is larger than ${}10$.
3. ${}x$ is smaller than ${}10$.
4. ${}x$ is a square number.
5. ${}x$ is not a square number.
6. ${}x$ is a prime number.
7. ${}x$ is not a prime number.
8. ${}x$ is the product of exactly two distinct prime numbers.

Create a solution