Chapter 2.11, Problem 11.1E

Write the following sentences using the quantifier notation (i.e., use the symbols $\exists$ and/or $\forall$). Note: We do not claim these statements are true, so please do not try to prove them!

1. Every integer is prime.
2. There is an integer that is neither prime nor composite.
3. There is an integer whose square is 2.
4. All integers are divisible by 5.
5. Some integer is divisible by 7.
6. The square of any integer is nonnegative.
7. For every integer x, there is an integer y such that $xy=1$.
8. There are an integer x and an integer y such that $x/y=10$.
9. There is an integer that, when multiplied by any integer, always gives the result 0.
10. No matter what integer you choose, there is always another integer that is larger.
11. Everybody loves somebody sometime.