Q60. - Algebra 2

Question

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

60. Every integer is a whole number.

Step-by-Step Solution

Answer

Given statement is False.

Counterexample is $-1$ as it is an integer but not a whole number.

Step 1 - 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.

Step 2 - Relationship between different sets

Following vein 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

Step 3 - Check given statement is true or false.

Using image of step 2, set of integers does not lies inside the set of whole numbers.

So given statement is false.

Example could be negative integers which are not whole number.

$-1$ is an integer but not a whole number.