Question

State whether the statement given in the question is true or False:

Every integer is a rational number but every rational number need not be an integer.

• A. True
• B. False

Answer 1

The correct option is A True

Determine the statement “Every integer is a rational number but every rational number need not be an integer”.

A rational number need not be an integer, but every integer is a rational number. We know that $1=\frac{1}{1},2=\frac{2}{1},3=\frac{3}{1},4=\frac{4}{1}$and so on…. also, $-1=\frac{-1}{1},-2=\frac{-2}{1},-3=\frac{-3}{1},-4=\frac{-4}{1}$and so on.
In other words, any integer a can be written as $a=\frac{a}{1}$, which is a rational number. Each integer is a rational number $\frac{3}{2},-\frac{5}{3}$, etc. are rational numbers without a doubt, but they are not integers.

Hence, the given statement is “True”.