Deductive and Inductive Flashcards

Which of the following BEST describes a counterexample in the context of deductive reasoning?

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.

Scientists notice that patients who take Drug X recover faster than those who don't. They conclude Drug X likely accelerates recovery. This is:

Answer: An inductive inference based on observed patterns

Drawing a probabilistic conclusion from observed data patterns is inductive reasoning.

Which argument contains the formal fallacy of denying the antecedent?

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'.

What is the key difference between a valid argument and a sound argument?

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.

In inductive reasoning, adding more confirming instances to a sample typically:

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.

All even numbers are divisible by 2. The number 48 is even. Therefore, 48 is divisible by 2. What type of argument is this?

Answer: A valid and sound deductive argument

This is a valid deductive argument (conclusion follows necessarily) and sound because both premises are true.

Which of the following is an example of statistical inductive reasoning?

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.