Exercise 18.
Simplifying negations will be especially useful in the next section when we try to prove a statement by considering what would happen if it were false. For each statement below, write the negation of the statement as simply as possible. Don't just say, “it is false that …”.
Every number is either even or odd.
There is a sequence that is both arithmetic and geometric.
For all numbers \(n\text{,}\) if \(n\) is prime, then \(n+3\) is not prime.