Question

which is a counterexample for the conditional statement shown?
if the numerator of a fraction is larger than the denominator of the fraction, then the fraction is greater than 1.
any fraction with a denominator of 0
any fraction with a numerator of 0
any fraction with a positive numerator and a negative denominator
any fraction with a negative numerator and a positive denominator

Explanation:

Step1: Analyze the conditional statement

The statement is: If numerator > denominator, then fraction > 1. A counterexample must satisfy numerator > denominator but result in fraction ≤ 1.

Step2: Evaluate each option

• Option1: Denominator=0 is undefined, not a valid fraction.
• Option2: Numerator=0: 0 < denominator (non-zero), doesn't satisfy numerator > denominator.
• Option3: Positive numerator, negative denominator: Let numerator $a>0$, denominator $b<0$. Then $a > b$ (positive > negative), and $\frac{a}{b} < 0 < 1$, which violates the conclusion.
• Option4: Negative numerator, positive denominator: Numerator $a<0$, denominator $b>0$, so $a < b$, doesn't satisfy the hypothesis.

Answer:

any fraction with a positive numerator and a negative denominator