Concept explainers
To state: The statement false by finding a counterexample: The reciprocal of each natural number is a natural number.
The statement is false.
Given information:
The given statement is the reciprocal of each natural number is a natural number.
Explanation:
Consider the definition of natural numbers:
Natural number includes all positive and whole numbers.
Now consider the statement: The reciprocal of each natural number is a natural number.
It is known that a number is said to be reciprocal of a given number if the product of this number and its reciprocal is 1.
Counterexample:
Take a natural number 8.
Reciprocal of 8 is
Therefore, the given statement is false.
Chapter 1 Solutions
High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11
- Algebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSONContemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
- Algebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSONIntroduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge PressCollege Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education