Single choice · #128
A parent says, “For a child to improve grades, they must work hard. Therefore, if they work hard, their grades will certainly improve.” What is the logical error in this reasoning?
Show answer & explanation
Answer: A
- ATreating a necessary condition as a sufficient condition✓ Correct. “Must work hard” only indicates that hard work is a necessary condition for improving grades; without hard work improvement won't happen, but even with hard work improvement is not guaranteed, as factors like methods, foundation, and state also matter.
- BTreating a sufficient condition as a necessary condition✗ Incorrect. The statement does not claim that hard work is anything more than indispensable; rather, it elevates a necessary condition to a sufficient one, which reverses the direction of the reasoning.
- CDenying the antecedent✗ Incorrect. Denying the antecedent would take the form “If one does not work hard, then grades will certainly not improve”; such a step does not appear, and the main issue is a confusion about the types of conditions.
- DAffirming the consequent✗ Incorrect. Affirming the consequent would have the form “If A then B; B is true; therefore A is true”; no such chain of reasoning is present here.
Explanation:“Must work hard” expresses that hard work is a necessary condition: improvement in grades implies hard work. But the parent then says “as long as one works hard, grades will certainly improve,” treating a necessary condition as a sufficient one—a common mistake. Hard work increases the probability of success but does not guarantee it.