CCTST Deductive Reasoning 5 ā Questions and Answers
Question 1: The argument form 'P ā Q; P; therefore Q' is called:
- Modus tollens
- Modus ponens (Correct answer)
- Disjunctive syllogism
- Hypothetical syllogism
Correct answer: Modus ponens
Modus ponens (affirming the antecedent) concludes Q when both PāQ and P are given.
Question 2: Some athletes are vegetarians. All vegetarians avoid red meat. Which conclusion must be true?
- All athletes avoid red meat
- Some athletes avoid red meat (Correct answer)
- No athletes eat red meat
- All vegetarians are athletes
Correct answer: Some athletes avoid red meat
The vegetarian athletes (some athletes) must avoid red meat, making 'some athletes avoid red meat' necessarily true.
Question 3: If a syllogism has a true conclusion, it must be valid. Which statement best identifies the flaw in this claim?
- It confuses validity with truth of premises
- A true conclusion can result from an invalid argument (Correct answer)
- Syllogisms cannot have true conclusions
- Validity requires false premises
Correct answer: A true conclusion can result from an invalid argument
An invalid argument can accidentally produce a true conclusion; validity concerns the argument's structure, not the conclusion's truth value.
Question 4: No one who cheats on exams graduates with honors. Taylor graduated with honors. What follows?
- Taylor cheated on exams
- Taylor did not cheat on exams (Correct answer)
- Taylor barely graduated
- Taylor's honors were revoked
Correct answer: Taylor did not cheat on exams
Modus tollens: honors graduation is incompatible with cheating, so an honors graduate cannot be a cheater.
Question 5: All X are Y. No Y are Z. Which conclusion follows with certainty?
- All Z are X
- No X are Z (Correct answer)
- Some X are Z
- All Y are X
Correct answer: No X are Z
X is a subset of Y, and Y excludes Z entirely; therefore X, being within Y, must also exclude Z.
Question 6: A deductive argument is 'sound' if and only if it is:
- Valid with at least one true premise
- Invalid but with a true conclusion
- Valid with all true premises (Correct answer)
- Invalid with all false premises
Correct answer: Valid with all true premises
Soundness requires both validity (correct logical structure) and all premises being actually true.
Question 7: If P then Q. If Q then R. P is true. What must be true?
- Only Q is true
- Only R is true
- Both Q and R are true (Correct answer)
- Neither Q nor R can be determined
Correct answer: Both Q and R are true
PāQ with P true gives Q; QāR with Q true gives R; both conclusions hold by successive modus ponens.
CCTST Deductive Reasoning 5
The argument form 'P ā Q; P; therefore Q' is called: