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Every natural number is integer true or false?

Every natural number is integer true or false?

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 9723 Points
10 days ago
In this type of question we have to use the concept of different sets of numbers. Firstly we have to consider the definition of natural numbers and integers. Then we will check the difference between natural numbers and integers. After that we have to verify the given statement. If the given statement is correct then we will say it is true, otherwise we will say that the given statement is false. Complete step-by-step solution: Now, we have to state whether the statement “Every natural number is integer” is true or false. Let us define the set of natural numbers and set of integers as follows: We can define the set of integers as the set of whole numbers (not a fractional number) that can be positive, negative and zero. It is denoted by Z . Hence, the set of integers is: ⇒Z={⋯⋯⋯,−3,−2,−1,0,1,2,3,⋯⋯⋯} We can define the set of natural numbers as the set of positive integers or counting numbers. It is denoted by N . Hence, the set of natural numbers is: ⇒N={1,2,3,4,5,⋯⋯⋯} By these definitions we can observe that the set of integers consists of whole numbers that can be positive, negative and zero whereas the set of natural numbers does not contains zero and negative integers that is {⋯⋯⋯,−3,−2,−1,0} . Thus we can say that the set of Integers is the union of the set of natural numbers and the set {⋯⋯⋯,−3,−2,−1,0} . This implies that all natural numbers are integers. Hence, the statement “Every natural number is integer” is True. Note: Students have to note that the natural numbers are the numbers we use in human life for counting purposes and hence they are also known as counting numbers. Also students have to take care when they use different types of sets. Students can use the definitions of sets to find out whether one set is a subset of another set or not. Also students have to verify whether the given statement is true or false.

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