Chapter A, Problem 1SE

To determine

Whether the sentence “All integers are real numbers” is a statement. If so, tell whether the statement is true or false.

Answer to Problem 1SE

The sentence “All integers are real numbers” is a $\underset{\_}{\text{statement}}$ and the statement is $\underset{\_}{\text{true}}$.

Explanation of Solution

The given sentence is “All integers are real numbers”.

A statement or a proposition is a declarative sentence which is either true or false.

Here, the sentence is a statement.

The integers are $0,\pm 1,\pm 2,\cdots$ and the real numbers are $\left(-\infty ,\infty \right)$.

The real numbers contain all the integers.

So that all integers are real numbers.

Hence, the statement is true.

Therefore, the sentence “All integers are real numbers” is a $\underset{\_}{\text{statement}}$ and the statement is $\underset{\_}{\text{true}}$.