CCTST Deductive Reasoning 2 — Questions and Answers
Question 1: All mammals are warm-blooded. No reptiles are warm-blooded. Which conclusion must follow?
- Some reptiles are mammals
- No reptiles are mammals (Correct answer)
- All warm-blooded animals are mammals
- Some mammals are reptiles
Correct answer: No reptiles are mammals
Since all mammals are warm-blooded and no reptiles are warm-blooded, no reptile can be a mammal.
Question 2: If it is raining, the ground is wet. The ground is not wet. What must be true?
- It is raining
- It is not raining (Correct answer)
- The ground is dry because it is sunny
- We cannot determine weather conditions
Correct answer: It is not raining
This is modus tollens: denying the consequent (ground not wet) allows us to deny the antecedent (not raining).
Question 3: Every student who passed the exam studied for at least five hours. Mia did not study for five hours. What can be concluded?
- Mia passed the exam
- Mia did not pass the exam (Correct answer)
- Mia studied for exactly four hours
- Nothing can be concluded about Mia
Correct answer: Mia did not pass the exam
Because studying five or more hours is necessary to pass, failing to meet that condition means Mia could not have passed.
Question 4: All A are B. All B are C. Which statement is necessarily true?
- All C are A
- All A are C (Correct answer)
- Some C are not A
- No A are C
Correct answer: All A are C
The chain All A→B and All B→C yields All A→C by the hypothetical syllogism.
Question 5: Either the server is down or the network is broken. The network is not broken. What follows?
- The server is down (Correct answer)
- The network is down
- Both the server and network are fine
- The server may or may not be down
Correct answer: The server is down
Disjunctive syllogism: when one disjunct is false, the other must be true.
Question 6: No licensed drivers are under 16 years old. Jordan is 14 years old. What must be true?
- Jordan is a licensed driver
- Jordan is not a licensed driver (Correct answer)
- Jordan will never drive
- Jordan has a learner's permit
Correct answer: Jordan is not a licensed driver
Because Jordan is under 16 and no one under 16 is a licensed driver, Jordan is not licensed.
Question 7: If a number is divisible by 6, it is divisible by both 2 and 3. The number 18 is divisible by 6. What follows?
- 18 is divisible by 2 but not 3
- 18 is divisible by 3 but not 2
- 18 is divisible by both 2 and 3 (Correct answer)
- 18 is not divisible by 2 or 3
Correct answer: 18 is divisible by both 2 and 3
Modus ponens applies: the antecedent is confirmed, so the consequent (divisibility by 2 and 3) must hold.
CCTST Deductive Reasoning 2
All mammals are warm-blooded.
No reptiles are warm-blooded.
Which conclusion must follow?