"If the plane takes off from the airstrip B then it is south bound. The plane…
2023
"If the plane takes off from the airstrip B then it is south bound. The plane did not take off from the airstrip B, therefore it is not southbound." Identify the formal fallacy in the above argument.
Answer: D. Denying the antecedent — ConceptIn a conditional statement P → Q, the premise guarantees Q only when P occurs. From ¬P, nothing follows about Q, because Q may still occur for some…
- A.
Exclusive premises
- B.
Fallacy of four terms
- C.
Affirming the consequent
- D.
Denying the antecedent
Show answer & explanation
Correct answer: D
Concept
In a conditional statement P → Q, the premise guarantees Q only when P occurs. From ¬P, nothing follows about Q, because Q may still occur for some other reason.
Application
Let P mean “the plane takes off from airstrip B” and Q mean “the plane is southbound.”
The first sentence gives P → Q.
The second premise gives ¬P, and the conclusion claims ¬Q.
Thus the argument has the pattern P → Q, ¬P, therefore ¬Q, which is denying the antecedent.
Cross-check
The plane could take off from another airstrip and still travel south. That counterexample makes both premises true while the conclusion is false, confirming that the inference is invalid.
Contrast
Exclusive premises concerns a categorical syllogism with two negative premises.
The fallacy of four terms concerns a categorical syllogism containing four distinct terms.
Affirming the consequent has the pattern P → Q, Q, therefore P.
Denying the antecedent has the pattern P → Q, ¬P, therefore ¬Q.
Therefore, the formal fallacy is denying the antecedent.