Questions: Deductive vs. Inductive Reasoning

Question 1

Which of the following is an example of deductive reasoning?

• A. I have seen 50 swans, all white, so all swans must be white.
• B. Every square has four right angles. This shape is a square. Therefore it has four right angles.
• C. My last three tests were A's, so I will probably get an A on the next test.
• D. The pattern 2, 4, 8, 16 doubles each time, so the next number is probably 32.

Answer: (B)

Option B moves from a general rule (all squares have four right angles) to a specific conclusion about a particular shape. The conclusion is guaranteed if the premises are true — that is deduction. Options A, C, and D all generalize from specific observations, which is induction — the conclusions are plausible but not guaranteed.

Question 2

Inductive reasoning can provide absolute certainty that a conclusion is true.

• T. True
• F. False

Answer: False

Inductive reasoning provides evidence and increases probability, but never guarantees certainty. No matter how many confirming cases you observe, there could always be an exception you have not seen. Only deductive reasoning — where the conclusion follows necessarily from the premises — provides absolute certainty (given true premises).

Question 3

A student notices that 3 + 5 = 8, 7 + 11 = 18, 13 + 17 = 30, and 19 + 23 = 42. She conjectures: 'The sum of any two odd primes is even.' Is her reasoning inductive or deductive? How could she turn it into a deductive argument?

Model answer: Her reasoning is inductive — she is generalizing from specific examples. To make it deductive, she could argue: every odd prime is odd; the sum of two odd numbers is always even (because odd + odd = even); therefore the sum of two odd primes is even.

The student's pattern-spotting is inductive reasoning at work: observing cases and forming a conjecture. The deductive version replaces the examples with a general rule (odd + odd = even) that covers all cases at once. The inductive approach discovers the pattern; the deductive approach proves it.