To write: A conditional statement, write a counterexample to the statement and explain reasoning.
Answer to Problem 49HP
Thestatement is “If the number given is prime, then the number is odd” and counterexample is “If the number given is prime, then the number can be even.”
Explanation of Solution
Given information:
The statement is conditional.
Calculation:
The conditional statement is “If the number given is prime, then the number is odd.”
In the above statement hypothesis is “the number given is prime” and conclusion is “the number is odd.”
The hypothesis is true for all the prime numbers. If the number given is 2, then the conclusion cannot be true because 2 is an even number.
So, the counterexample is as follows.
“If the number given is prime, then the number can be even.”
Therefore, the statement is “If the number given is prime, then the number is odd” and counterexample is “If the number given is prime, then the number can be even.”
Chapter 1 Solutions
Algebra 1
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