Statements

The following is the list of problems for Section 2.1 of the Book of Proof (page 37). There is a forum open at the end, so you can ask questions. It is a great way to interact with the instructor and with other students in your class, should you need some assistance with any question. Please, do not post solutions.

Decide whether or not the following are statements. In the case of a statement, say if it is true or false, if possible.

1. Every real number is an even integer.
2. Every even integer is a real number.
3. If \( x \) and \( y \) are real numbers and \( 5x=5y \), then \( x = y \).
4. Sets \( \mathbb{Z} \) and \( \mathbb{N} \).
5. Sets \( \mathbb{Z} \) and \( \mathbb{N} \) are infinite.
6. Some sets are finite.
7. The derivative of any polynomial of degree 5 is a polynomial of degree 6.
8. \( \mathbb{N} \not\in \mathscr{P}(\mathbb{N}) \).
9. \( \cos(x) = -1 \).
10. \( (\mathbb{R} \times \mathbb{N} ) \cap (\mathbb{N} \times \mathbb{R}) = \mathbb{N} \times \mathbb{N} \).
11. The integer \( x \) is a multiple of 7.
12. If the integer \( x \) is a multiple of 7, then it is divisible by 7.
13. Either \( x \) is a multiple of 7, or it is not.
14. Call me Ishmael.
15. In the beginning, God created the heaven and the earth.