Question

If

$p:$ All integers are rational numbers and

$q:$ Every rational number is an integer

Then which of the following statement is correct?

• A. $p$ is false and $q$ is true
• B. $p$ is true and $q$ is false
• C. Both $p$ and $q$ are true.
• D. Both $p$ and $q$ are false.

Answer 1

Answer: (B)

$p$ is true and $q$ is false

Integers are $....-4,-3,-2,-1,0,1,2,\mathrm{3...}$ and so on.
Rational numbers are those numbers which can be expressed in the form $\frac{p}{q}$, where $p$ and $q$ are integers and $q\ne 0$

We can write $-2$ as $\frac{-2}{1}$ and $3$ as $\frac{3}{1}$

Hence, some rational numbers are integers.

Few Rational numbers are not integers.

For example, $\frac{8}{11},\frac{3}{7},\frac{2}{3}$ and $\frac{5}{7}$

Hence, $p$ is true and $q$ is false.