# MATH 300 Fall 2018 Assignment 06

## 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.

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