what value is a counterexample for the conditional statement shown? if a number between 0 and 100 is an odd…

what value is a counterexample for the conditional statement shown? if a number between 0 and 100 is an odd perfect square, then the only factors of the number are 1, the number itself, and the square root of the number. 9 25 49 81

what value is a counterexample for the conditional statement shown? if a number between 0 and 100 is an odd perfect square, then the only factors of the number are 1, the number itself, and the square root of the number. 9 25 49 81

Answer

Explanation:

Step1: Analyze the factors of 9

The factors of 9 are 1, 3, 9. Here 3 is a factor other than 1, 9 and its square - root (square - root of 9 is 3, but we are looking for non - trivial additional factors).

Step2: Analyze the factors of 25

The factors of 25 are 1, 5, 25. Here 5 is the square - root of 25, and the only non - trivial factor is the square - root as required by the statement.

Step3: Analyze the factors of 49

The factors of 49 are 1, 7, 49. Here 7 is the square - root of 49, and the only non - trivial factor is the square - root as required by the statement.

Step4: Analyze the factors of 81

The factors of 81 are 1, 3, 9, 27, 81. But 9 is the square - root of 81, and among the non - square - root factors, we need to check if it violates the statement. The non - square - root factors 3 and 27 make it not a counter - example as they don't follow the simple factor pattern of the statement in the wrong way.

Answer:

A. 9