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

what value is a counterexample for the conditional statement shown?\nif 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.\n9\n25\n49\n81

what value is a counterexample for the conditional statement shown?\nif 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.\n9\n25\n49\n81

Answer

Explanation:

Step1: Recall counterexample definition

A counterexample is a case where the hypothesis is true (number is odd perfect square between 0 - 100) but the conclusion is false (has more factors than 1, itself, and its square root).

Step2: Analyze each option

  • 9: Factors of 9 are 1, 3, 9. Square root is 3. Factors are 1, 3, 9 (matches conclusion). Not a counterexample.
  • 25: Factors of 25 are 1, 5, 25. Square root is 5. Factors are 1, 5, 25 (matches conclusion). Not a counterexample.
  • 49: Factors of 49 are 1, 7, 49. Square root is 7. Factors are 1, 7, 49 (matches conclusion). Not a counterexample.
  • 81: Factors of 81 are 1, 3, 9, 27, 81. Square root is 9. It has factors (3, 27) beyond 1, 81, and 9. Hypothesis is true (odd perfect square 0 - 100), conclusion is false. So 81 is a counterexample.

Answer:

81