Lesson 2.1 Inductive Reasoning and Conjectures

Front

What is inductive reasoning?

Back

Inductive reasoning is the process of observing patterns and making generalizations or conjectures based on those observations.

Front

What is a counterexample?

Back

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

Front

Provide a counterexample to the statement: 'If an animal is furry, then it is a hamster.'

Back

A cat is a counterexample because it is furry but not a hamster.

Front

How many squares are in a figure with 11 squares?

Back

There are 11 squares in the figure.

Front

What is the conjecture regarding the product of two odd numbers?

Back

The product of any two odd numbers is odd.

Front

What does the statement 'For all numbers a, 2a + 7 ≤ 17' imply?

Back

It implies that for any value of 'a', the expression 2a + 7 should not exceed 17.

Front

What is an example of a number that serves as a counterexample to the statement 'For all numbers a, 2a + 7 ≤ 17'?

Back

a = 6 is a counterexample because 2(6) + 7 = 19, which is greater than 17.

Front

What is the difference between inductive reasoning and deductive reasoning?

Back

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

Front

What is a conjecture?

Back

A conjecture is a statement that is believed to be true based on observations but has not yet been proven.

Front

How can patterns be used in inductive reasoning?

Back

Patterns can be observed in data or sequences, allowing individuals to make predictions or conjectures about future occurrences.