Question

Every rational number is an integer.
A.True
B.False

Answer 1

Hint: To answer this question we will analyze the definitions of a rational number and an integer. From the definition, we will check if the statement is true or false. We can also take examples of integers and rational numbers and see if they satisfy the condition.

Complete step-by-step answer:
First, we will look at the definition of an integer:-
An integer is any number that can be represented as a whole; that is integers are those numbers that can be expressed without a fractional component or a decimal component. Integers can be positive, negative or 0.
Some examples of integers are \[ - 1\] , \[ - 2\], \[ - 3\], 0, 1, 2 , etc.
Now, let us have a look at the definition of a rational number:-
A rational number is a number that can be expressed in the form \[\dfrac{p}{q}\] where \[p\] and \[q\] are integers and \[q \ne 0\]. Integer \[q\]can’t be equal to 0 because a fraction with denominator 0 is not defined. Some examples of rational numbers are \[\dfrac{1}{2}\], \[\dfrac{3}{2}\], 0, \[\dfrac{{ - 5}}{6}\], etc.
We can see from the examples that every rational number is not an integer because all rational numbers are expressed as fractions and not as whole. For example, \[\dfrac{1}{2}\] is equal to \[0.5\] is a rational number but not an integer.
So, the given statement is false.

Note: We must be careful that the converse of this statement is true. All rational numbers are not integers but all integers are rational numbers. This is because every integer \[p\] can be expressed in the form \[\dfrac{p}{1}\]. For example, the integer \[ - 2\] can be expressed as \[\dfrac{{ - 2}}{1}\] which is a rational number because both numerator and denominator are integers and the denominator is not equal to 0.