Identify the common pattern of deductive reasoning in the following argument:…
2023
Identify the common pattern of deductive reasoning in the following argument:
"If we don't stop for gas soon, then we will run out of gas. If we run out of gas, then we will be late for the wedding. Therefore, if we don't stop for gas soon, we will be late for the wedding."
Answer: D. Chain argument — ConceptA conditional argument can be classified by translating each statement into symbols and checking how the premises combine. When two implications share…
- A.
Denying the consequent
- B.
Affirming the consequent
- C.
Denying the antecedent
- D.
Chain argument
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Correct answer: D
Concept
A conditional argument can be classified by translating each statement into symbols and checking how the premises combine.
When two implications share a middle proposition, the chain rule (hypothetical syllogism) composes p → q and q → r to infer p → r.
Application
Let p mean “we do not stop for gas soon”, q mean “we run out of gas”, and r mean “we are late for the wedding”.
The first premise has the form p → q.
The second premise has the form q → r.
Composing the two implications removes the shared middle proposition q and gives p → r, exactly the stated conclusion.
Cross-check and contrast
Denying the consequent would require p → q together with ¬q to infer ¬p; those negated premises are absent.
Affirming the consequent would require p → q together with q to infer p; the argument does not reverse an implication in that way.
Denying the antecedent would require p → q together with ¬p to infer ¬q; that form is also absent.
The two linked implications and the conclusion p → r fit the chain rule.
Therefore, the pattern is a Chain argument, also called hypothetical syllogism.