Question

What is a counterexample to the conditional statement: "If an odd number is greater than 1 and less than 10, then it has no other factors than 1 and itself"?

a) 11
b) 9
c) 7
d) 5

Answer 1

The counterexample to the given statement is option (b) 9, as it is an odd number greater than 1 and less than 10 but has a factor other than 1 and itself (3).

Step-by-step explanation:

A counterexample to the conditional statement "If an odd number is greater than 1 and less than 10, then it has no other factors than 1 and itself" is an example of an odd number within that range that does have other factors aside from 1 and itself. Option (b) 9 is such an example because 9 is an odd number greater than 1 and less than 10, and has factors other than 1 and itself, which are 3 and 9 (since 3 x 3 = 9).