Question at position 5 The car is either electric, gasoline-powered, or hydrogen-powered. It is not electric. It is not hydrogen-powered. Therefore, it is gasoline-powered.Categorical Syllogism; Invalid; UnsoundBy Authority; Weak; UncogentInductive Generalization; Strong; ColgenBy elimination argument; Valid; Sound单项选择题
A
Categorical Syllogism; Invalid; Unsound
B
By Authority; Weak; Uncogent
C
Inductive Generalization; Strong; Colgen
D
By elimination argument; Valid; Sound

Question

Question at position 5 The car is either electric, gasoline-powered, or hydrogen-powered. It is not electric. It is not hydrogen-powered. Therefore, it is gasoline-powered.Categorical Syllogism; Invalid; UnsoundBy Authority; Weak; UncogentInductive Generalization; Strong; ColgenBy elimination argument; Valid; Sound单项选择题

A

Categorical Syllogism; Invalid; Unsound

B

By Authority; Weak; Uncogent

C

Inductive Generalization; Strong; Colgen

D

By elimination argument; Valid; Sound

BlackTom AI · Accepted Answer

This is a disjunctive elimination (also called an elimination or disjunctive syllogism) argument because it starts with a disjunction and eliminates alternatives to reach the remaining disjunct.

1. Relevant concepts
- Disjunction: a statement of the form A ∨ B ∨ C (at least one is true).
- Disjunctive elimination (by elimination): from (A ∨ B ∨ C) together with ¬A and ¬C, infer B.
- Validity: an argument form is valid if it is impossible for the premises to be true and the conclusion false.
- Soundness: an argument is sound if it is valid and its premises are actually true.

2. Step-by-step reasoning (formal)
Premises:
1. E ∨ G ∨ H (the car is either electric (E), gasoline (G), or hydrogen (H)).
2. ¬E (it is not electric).
3. ¬H (it is not hydrogen).

Derivation:
4. From (1) and (2): since E is false, the disjunction reduces to G ∨ H. (Disjunctive simplification)
5. From (4) and (3): since H is false, the remaining disjunct must be G. Therefore, G (the car is gasoline-powered).

3. Validity demonstration (intermediate reasoning)
Assume premises (1), (2), (3) are all true but suppose the conclusion G is false. Then E is false (from 2), H is false (from 3), and G is false (assumed). That makes E ∨ G ∨ H false, contradicting premise (1). Hence no valuation makes the premises true and conclusion false — the form is valid.

4. Soundness explanation
Because the argument is valid and its conclusion follows necessarily from the premises, if the premises are true in fact, the conclusion is true; thus the argument is sound.

5. Why other choices are incorrect
- Categorical syllogism: involves universal/particular categorical propositions (All, No, Some). The given argument is a disjunction, not categorical form.
- By authority: would cite an authority; none is cited here.
- Inductive generalization: would generalize from sample to population; this argument makes a deductive elimination, not an inductive generalization.