2.1 Inductive reasoning, conjectures, and counterexamples

Front

What is inductive reasoning?

Back

Inductive reasoning is a method of reasoning in which a general conclusion is drawn from specific examples or patterns.

Front

Define conjecture in mathematics.

Back

A conjecture is an unproven statement or hypothesis that is based on observations or patterns.

Front

What is a counterexample?

Back

A counterexample is an example that disproves a statement or conjecture.

Front

Find the next number in the sequence: 5, -10, 15, -20, ________

Back

25

Front

What is a valid counterexample for the statement: 'If an animal is a panther, then it lives in the forest.'?

Back

It lives in a zoo.

Front

Which is a counterexample of: If a four-sided shape has two sides the same length, then it must be a rectangle?

Back

Square.

Front

Which number is a counterexample to the statement: 'All numbers that are divisible by 2 are divisible by 4'?

Back

42.

Front

Make a conjecture about the next item in the sequence: 12, 6, 3, 1.5, 0.75, . . . . .

Back

Divide the previous number by 2.

Front

What is the difference between inductive and deductive reasoning?

Back

Inductive reasoning involves making generalizations based on specific instances, while deductive reasoning involves drawing specific conclusions from general principles.

Front

Provide an example of a conjecture.

Back

If a number is even, then it is divisible by 2.