HiSET: Math : Identify examples and counterexamples of concepts

Study concepts, example questions & explanations for HiSET: Math

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Example Questions

Example Question #1 : Identify Examples And Counterexamples Of Concepts

Consider the following statement:

"If an integer is odd and is between 10 and 20, then it must be prime."

Which of the following is a counterexample to the statement?

Possible Answers:

The integer 16 is not prime. 

The integer 9 is not prime. 

The integer 15 is not prime. 

The integer 13 is prime. 

Odd numbers are not evenly divisible by 2. 

Correct answer:

The integer 15 is not prime. 

Explanation:

A counterexample is a single example that disproves a statement. In order to disprove "If an integer is odd and is between 10 and 20, then it must be prime," you must show that there is an integer that is odd and is between 10 and 20, but is not prime. 

While 9 is odd and is not prime, it is not between 10 and 20. 16 is also not prime, but it is not odd.

15 is the answer because it is odd and is between 10 and 20, but is not prime, because it is divisible by 5 and 3, in addition to being divisible by itself and 1. 

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