CCTST Inductive Reasoning 3 — Questions and Answers
Question 1: A child touches a hot stove and gets burned. She touches it again and gets burned. She concludes that touching the stove always causes burns. This is an example of:
- Hypothetical syllogism
- Enumerative induction (Correct answer)
- Modus ponens
- Disjunctive syllogism
Correct answer: Enumerative induction
Enumerative induction involves observing repeated instances of a pattern and generalizing to a universal rule.
Question 2: Which factor does NOT affect the strength of an inductive argument?
- Sample size
- Sample diversity
- Whether the argument uses formal notation (Correct answer)
- Absence of known counter-examples
Correct answer: Whether the argument uses formal notation
Formal notation is a feature of deductive logic; inductive strength depends on evidential factors like sample quality.
Question 3: An argument concludes: 'Since this coin landed heads 9 times in a row, it will probably land tails next.' This is an example of the:
- Gambler's fallacy (Correct answer)
- Hasty generalization
- False dilemma
- Post hoc fallacy
Correct answer: Gambler's fallacy
The gambler's fallacy assumes past random events influence future independent events, which they do not.
Question 4: A scientist observes that plants in a greenhouse grow faster when classical music is played. She repeats the experiment 20 times with the same result. Her best next step to strengthen the inductive argument is to:
- Accept the conclusion as certain
- Test with varied plant species and music types (Correct answer)
- Reduce the sample to eliminate noise
- Replace induction with deduction
Correct answer: Test with varied plant species and music types
Testing varied conditions improves the generalizability and strength of an inductive conclusion.
Question 5: A journalist interviews 5 residents of Beverly Hills and concludes that all Californians are wealthy. This argument is weak primarily because:
- Beverly Hills residents lie in surveys
- The sample is too small and unrepresentative (Correct answer)
- Wealth cannot be measured
- California is too large to study
Correct answer: The sample is too small and unrepresentative
A small, geographically and economically unrepresentative sample cannot support a generalization about all Californians.
Question 6: Which of the following is the best example of a strong inductive argument?
- All mammals are warm-blooded; whales are mammals; therefore whales are warm-blooded
- I met two rude Parisians, so all Parisians must be rude
- In 500 random trials, 498 produced the predicted result, so the hypothesis is well-supported (Correct answer)
- Either it rains or it doesn't; it didn't rain; so it must have been sunny
Correct answer: In 500 random trials, 498 produced the predicted result, so the hypothesis is well-supported
A large number of consistent trials with a random sample provides strong inductive support for a hypothesis.
Question 7: The phrase 'inductive leap' refers to:
- A logical error that invalidates the argument
- Moving from specific observations to a general conclusion (Correct answer)
- Jumping to a deductive conclusion without premises
- Skipping steps in a mathematical proof
Correct answer: Moving from specific observations to a general conclusion
An inductive leap is the inferential move from observed specifics to a broader generalization or explanation.
CCTST Inductive Reasoning 3
A child touches a hot stove and gets burned.
She touches it again and gets burned.
She concludes that touching the stove always causes burns.
This is an example of: