Single choice · #804
During a design review, the art teacher had earlier reminded everyone: “If what is drawn is a square, then what is drawn is a quadrilateral.” After Xiaolin uploaded his sketch, the image recognition system indicated: what is drawn is a quadrilateral. He immediately said: “So what is drawn is a square.” Can this conclusion be validly drawn from what was said?
Show answer & explanation
Answer: C
- AThe reasoning holds, because a square is by definition a quadrilateral, and the system's result confirms exactly that.✗ It is true that every square is a quadrilateral, but the converse does not follow: a quadrilateral need not be a square. This option mistakes confirmation of the consequent for valid inference.
- BThe reasoning is flawed, because it commits the error of inferring “if it is not a square, then it is not a quadrilateral.”✗ That error (denying the antecedent) is a real one, but Xiaolin did not reason from “not a square” to “not a quadrilateral,” so this mischaracterizes his actual mistake.
- CThe conclusion does not follow: the drawing could also be a rectangle, a trapezoid, or some other quadrilateral, so it need not be a square.✓ There are many kinds of quadrilateral the system could have detected, so this single result alone cannot establish that the drawing is a square. This correctly identifies the fallacy of affirming the consequent.
- DThe reasoning is flawed, because the image recognition system may lack sufficient resolution and its detection data may be inaccurate.✗ This merely questions the reliability of the system's data; it never addresses whether the conclusion could be drawn even if the data were perfectly accurate.
Explanation:The inference is invalid. Every square is necessarily a quadrilateral, but quadrilaterals also include rectangles, trapezoids, and other irregular four-sided figures. Even if the system accurately reports that the drawing is a quadrilateral, it does not follow that the drawing is a square; a counterexample is a drawing that is in fact a rectangle or a trapezoid. Reasoning from the truth of the consequent back to the antecedent is the formal fallacy known as affirming the consequent.