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91Ó°ÊÓ

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

Every whole number is an integer

Short Answer

Expert verified

Given statement is true.

Step by step solution

01

- Define different sets 

  • The set 1,2,3,4,5,... is called the set of natural number.
  • The set 0,1,2,3,4,5,... is called the set of whole number.
  • The set -3,-2,-1,0,1,2,3,...is called the set of integer number.
  • The set of rational number has numbers in the ratio form mn, 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.
02

- 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

03

- Check given statement is true or false.

Using image of step 2, set of whole number lies inside the set of integers.

So given statement is true.

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