Question

Determine whether each of the following sentences is a proposition: If the sentence is a proposition, then write its negation:

1. Every prime number is even.
2. There is a number that is larger than $17$.

Answer 1

Write the negation for:

Every prime number is even:

There is a number that is larger than $17$.

Step 1: Every prime number is even:

A proposition is a sentence that is either true or false.

The given statement is false as every prime number is not an even number.

Negation of the given sentence is “every prime number is not an even number.”

Step 2: There is a number that is larger than $17.$

The given statement is a proposition as there are many numbers that are larger than $17$ and the statement is true.

Negation of the given sentence is “there is no number larger than$17$.”

Hence, the negation for the given sentences are:

1. Every prime number is not an even number.
2. There is no number larger than$17$.