CCTST Deductive and Inductive 3 — Questions and Answers
Question 1: Which of the following BEST describes a counterexample in the context of deductive reasoning?
- An example that makes the conclusion more likely
- A case where the premises are true but the conclusion is false (Correct answer)
- An example that supports the general rule
- A premise that contradicts another premise
Correct answer: A case where the premises are true but the conclusion is false
A counterexample demonstrates invalidity by showing a case where premises are true yet the conclusion is false.
Question 2: Scientists notice that patients who take Drug X recover faster than those who don't. They conclude Drug X likely accelerates recovery. This is:
- A deductive proof that Drug X works
- An inductive inference based on observed patterns (Correct answer)
- A necessary conclusion from logical premises
- An invalid argument because correlation isn't causation
Correct answer: An inductive inference based on observed patterns
Drawing a probabilistic conclusion from observed data patterns is inductive reasoning.
Question 3: Which argument contains the formal fallacy of denying the antecedent?
- If you study, you pass. You studied. So you pass.
- If you study, you pass. You didn't study. So you won't pass. (Correct answer)
- If you study, you pass. You passed. So you studied.
- You always pass when you study. You're studying. So you'll pass.
Correct answer: If you study, you pass. You didn't study. So you won't pass.
Denying the antecedent incorrectly concludes that because P is false, Q must also be false in 'If P then Q'.
Question 4: What is the key difference between a valid argument and a sound argument?
- A valid argument has true premises; a sound argument has true conclusions
- A valid argument's conclusion follows from its premises; a sound argument is also valid with true premises (Correct answer)
- A sound argument is inductive; a valid argument is deductive
- A valid argument is always sound; soundness adds nothing
Correct answer: A valid argument's conclusion follows from its premises; a sound argument is also valid with true premises
Validity means the conclusion follows necessarily from the premises; soundness additionally requires the premises to actually be true.
Question 5: In inductive reasoning, adding more confirming instances to a sample typically:
- Makes the argument deductively valid
- Weakens the inductive strength of the argument
- Increases the strength of the inductive inference (Correct answer)
- Has no effect on the argument's strength
Correct answer: Increases the strength of the inductive inference
More confirming instances from a diverse sample generally strengthen an inductive argument by increasing the probability of the conclusion.
Question 6: All even numbers are divisible by 2. The number 48 is even. Therefore, 48 is divisible by 2. What type of argument is this?
- A strong inductive argument
- A weak inductive argument
- A valid and sound deductive argument (Correct answer)
- An invalid deductive argument
Correct answer: A valid and sound deductive argument
This is a valid deductive argument (conclusion follows necessarily) and sound because both premises are true.
Question 7: Which of the following is an example of statistical inductive reasoning?
- All A are B; x is A; therefore x is B
- 78% of surveyed voters prefer Candidate X; therefore X will probably win (Correct answer)
- If the law applies to all, and you are subject to law, then the law applies to you
- Either it rains or it doesn't; it doesn't rain; so it does not rain
Correct answer: 78% of surveyed voters prefer Candidate X; therefore X will probably win
Using sample statistics to draw a probable conclusion about a population is a classic form of statistical inductive reasoning.
CCTST Deductive and Inductive 3
Which of the following BEST describes a counterexample in the context of deductive reasoning?