Question at position 24 Argument:P1: Either the student followed a study plan or failed the exam.P2: The student did not follow a study plan.C: Therefore, the student failed the exam. This argument is:Invalid (Affirming a disjunct)Valid (by elimination/Disjunctive Syllogism)Valid (Modus Ponens)Invalid (Denying the antecedent)Single choice
A
Invalid (Affirming a disjunct)
B
Valid (by elimination/Disjunctive Syllogism)
C
Valid (Modus Ponens)
D
Invalid (Denying the antecedent)

Question

Question at position 24 Argument:P1: Either the student followed a study plan or failed the exam.P2: The student did not follow a study plan.C: Therefore, the student failed the exam. This argument is:Invalid (Affirming a disjunct)Valid (by elimination/Disjunctive Syllogism)Valid (Modus Ponens)Invalid (Denying the antecedent)Single choice

A

Invalid (Affirming a disjunct)

B

Valid (by elimination/Disjunctive Syllogism)

C

Valid (Modus Ponens)

D

Invalid (Denying the antecedent)

BlackTom AI · Accepted Answer

Disjunctive syllogism has the form "A or B; not A; therefore B," which matches this argument exactly.

1. Relevant knowledge points and concepts
- Disjunction (A ∨ B): a statement claiming at least one of A or B is true.
- Negation (¬A): the denial of a proposition.
- Disjunctive syllogism (also called proof by elimination): from A ∨ B and ¬A infer B. This is a valid logical rule.
- Common fallacies to contrast: affirming a disjunct (A ∨ B; A; therefore B) and denying the antecedent (If A → B; ¬A; therefore ¬B), both invalid forms. Modus Ponens is a different valid form (A → B; A; therefore B).

2. Step-by-step reasoning mapping premises to the form
- Let S = "the student followed a study plan."
- Let F = "the student failed the exam."
- P1: Either the student followed a study plan or failed the exam. This is S ∨ F.
- P2: The student did not follow a study plan. This is ¬S.
- Conclusion: Therefore, the student failed the exam. This is F.

3. Intermediate steps / formal application
- From P1 and P2 we have S ∨ F and ¬S.
- Disjunctive syllogism permits the inference: from S ∨ F and ¬S infer F.
- Thus the conclusion F follows logically and validly.

4. Why the correct answer is correct
- Given the disjunction and the denial of one disjunct, the other disjunct must be true if the disjunction is true. There is no reliance on conditional structure or additional assumptions. This is precisely the rule of elimination (disjunction elimination).

5. Why the other options are incorrect
- "Invalid (Affirming a disjunct)" describes the fallacy A ∨ B; A; therefore B, which is not this form (here we negate S, not affirm it).
- "Valid (Modus Ponens)" is a different valid form requiring a conditional (A → B) and A; we have no conditional premise here.
- "Invalid (Denying the antecedent)" refers to the invalid form If A → B; ¬A; therefore ¬B, which does not match these premises.

6. Conclusion
The argument is valid by elimination (Disjunctive Syllogism). This confirms the provided answer: "Valid (by elimination/Disjunctive Syllogism)."