Question

indicate whether the following statement is true or false.
every integer is a rational number.
choose the correct answer below.
a. true, because \\(\frac{p}{1} = p\\) for any integer \\(p\\).
b. true, because integers include positive as well as negative counting numbers.
c. false, because integers cannot be written in the form \\(\frac{p}{q}\\), where \\(q \
eq 0\\).
d. false, because integers do not include negative counting numbers.

Explanation:

A rational number is defined as a number that can be expressed as $\frac{p}{q}$ where $p$ and $q$ are integers and $q
eq0$. For any integer $p$, we can write it as $\frac{p}{1}$ (since $1
eq0$), so every integer fits the definition of a rational number. Option A correctly explains this by showing that any integer $p$ can be written as $\frac{p}{1}$, which is a rational number. Option B's reasoning is incorrect because the inclusion of positive/negative counting numbers doesn't directly relate to being rational. Option C is false as integers can be written in $\frac{p}{q}$ form. Option D is false as integers do include negative counting numbers (negative integers).

Answer:

A. True, because $\frac{p}{1} = p$ for any integer $p$.