CCTST Deductive and Inductive 4 — Questions and Answers
Question 1: A student argues: 'My three friends all failed this professor's class. This professor must be an unfair grader.' This argument is BEST described as:
- A valid deductive argument
- A hasty generalization — a weak inductive argument (Correct answer)
- A sound argument with true premises
- A modus tollens argument form
Correct answer: A hasty generalization — a weak inductive argument
Generalizing from only three cases to a conclusion about the professor's grading overall is a hasty generalization, a weak inductive argument.
Question 2: Which is the correct form of modus tollens?
- If P then Q; P; therefore Q
- If P then Q; not Q; therefore not P (Correct answer)
- If P then Q; not P; therefore not Q
- If P then Q; Q; therefore P
Correct answer: If P then Q; not Q; therefore not P
Modus tollens takes the form: If P then Q; Q is false; therefore P is false — a valid deductive form.
Question 3: An argument by analogy concludes that because two things share several properties, they share another property. This type of reasoning is:
- Deductive, since analogies guarantee conclusions
- A form of inductive reasoning that varies in strength (Correct answer)
- Always fallacious because analogies are imperfect
- Formal deductive logic expressed informally
Correct answer: A form of inductive reasoning that varies in strength
Analogical reasoning is inductive because its conclusions are probable based on shared features, not logically guaranteed.
Question 4: Consider: 'Whenever pressure increases in a gas, temperature rises (in a sealed container). We increased the pressure. Therefore the temperature rose.' This is:
- A weak inductive generalization
- A valid deductive argument from a scientific law (Correct answer)
- A fallacy of affirming the consequent
- An analogical argument
Correct answer: A valid deductive argument from a scientific law
Applying an established law (the premise) to a specific case and deducing the outcome is deductive reasoning.
Question 5: What does it mean to say that deductive arguments are 'truth-preserving'?
- They preserve the exact wording of the premises in the conclusion
- If the premises are true, a valid deductive argument guarantees the conclusion is true (Correct answer)
- They always start with true premises
- The conclusion repeats one of the premises
Correct answer: If the premises are true, a valid deductive argument guarantees the conclusion is true
Truth-preserving means valid deductive reasoning cannot lead from true premises to a false conclusion.
Question 6: Which of the following would WEAKEN an inductive generalization the most?
- Increasing the sample size significantly
- Discovering that the sample is biased or unrepresentative (Correct answer)
- Finding additional confirming instances
- Restating the conclusion more cautiously
Correct answer: Discovering that the sample is biased or unrepresentative
A biased or unrepresentative sample undermines the foundation of an inductive generalization, making it much weaker.
Question 7: Which correctly identifies a difference between inductive and deductive reasoning regarding certainty?
- Both yield certain conclusions when premises are true
- Deductive reasoning yields necessary conclusions; inductive reasoning yields probable ones (Correct answer)
- Inductive reasoning is more reliable than deductive reasoning
- Deductive reasoning deals with probability while inductive reasoning deals with certainty
Correct answer: Deductive reasoning yields necessary conclusions; inductive reasoning yields probable ones
In valid deductive reasoning the conclusion is necessarily true given true premises; inductive conclusions are only probably true.
CCTST Deductive and Inductive 4
A student argues: 'My three friends all failed this professor's class.
This professor must be an unfair grader.' This argument is BEST described as: