Concept explainers
To find: the converse, inverse, and contrapositive of the given statement.
Answer to Problem 17CYU
Theconverse and inverse of the statement is false and contrapositive is true.
Explanation of Solution
Given information:
The statement is given “All whole numbers are integers”.
Consider the given statement in such manner.
Let a number is whole can be denoted by
Converse of the statement is “if a number is an integer, then it is a whole number”
Which is false.
Counterexample:
Find the inverse of the statement.
The inverse of the statement is “if a number is not whole, then it is not integer”
Which is the false.
Counterexample:
Find the contrapositive of the statement.
The contrapositive of the statement is “if a number is not an integer, then it is not whole number”
Which is true because integer are like whole numbers, but they also include negative numbers. So, if the number is not an integer, then it can say that number is also not a whole.
Therefore, theconverse and inverse of the statement is false and contrapositive is true.
Chapter 2 Solutions
Geometry, Student Edition
Additional Math Textbook Solutions
University Calculus: Early Transcendentals (4th Edition)
Trigonometry (11th Edition)
College Algebra (7th Edition)
Thomas' Calculus: Early Transcendentals (14th Edition)
Calculus: Early Transcendentals (3rd Edition)
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