# MATH 300 Fall 2018 Assignment 07

## And, Or, Not

The following is the list of problems for Section 2.2 of the

*Book of Proof*(page 41). 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**.Express each statement or open sentence in one of the forms \( P \lor Q, P \land Q \), or \( \lnot P \). Be sure to also state exactly what statements \( P \) and \( Q \) stand for.

- The number 8 is both even and a power of 2.
- The matrix \( A \) is not invertible.
- \( x \neq y \)
- \( x < y \)
- \( x \geq y \)
- There is a quiz scheduled for Wednesday or Friday.
- The number \( x \) equals zero, but the number \( y \) does not.
- At least one of the numbers \( x \) or \( y \) equals zero.
- \( x \in A \setminus B \)
- \( x \in A \cup B \)
- \( A \in \{ X \in \mathscr{P}(\mathbb{N}) : \lvert X^\complement \rvert < \infty \} \)
- Happy families are all alike, but each unhappy family is unhappy in its own way. (Leo Tolstoy,
*Anna Karenina*) - Human beings want to be good, but not too good, and not all the time. (George Orwell)
- A man should look for what it is, and not for what he thinks should be. (Albert Einstein)