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Big Ideas Math Integrated I, 2016 View details

2. Inductive and Deductive Reasoning

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Exercise 32 Page 457

What do you use to claim that 12 is a rational number?

Deductive reasoning, see solution.

Practice makes perfect

Let's first determine the difference between inductive and deductive reasoning.

Inductive reasoning means we find a pattern to prove something.
Deductive reasoning requires us to prove something by facts and definitions.

The two first sentences state the definition of rational and irrational numbers. Using these definitions, we can claim that 12 is a rational number. Since established definitions and the laws of logic were used to reach a conclusion, this is an example of deductive reasoning.