Question

Determine whether each statement is true or false. If false, give a counterexample.

Every integer is a rational number.

Short answer

Given statement is true.

Step-by-step solution

- Define different sets 

• The set $\left\{1,2,3,4,5,...\right\}$ is called the set of natural number.
• The set $\left\{0,1,2,3,4,5,...\right\}$ is called the set of whole number.
• The set $\left\{-3,-2,-1,0,1,2,3,...\right\}$ is called the set of integer number.
• The set of rational number has numbers in the ratio form $\frac{m}{n}$, where m and n are integers and n is non-zero. The decimal form of a rational number is either a terminating or repeating decimal.
• A real number that is not rational is irrational. The decimal form of an irrational number is neither terminating nor rational.
• Combine sets of rational and irrational number is real number.

- Relationship between different sets

Following venn diagram shows relationship between different sets

Where, the symbols denote

N- Natural number

W- Whole number

Z- Integers

Q- Rational number

I- Irrational number

R- Real numbers

- Check given statement is true or false.

Using image of step 2, set of integers lies inside the set of rational numbers.

So given statement is true.