Inductive and Deductive Reasoning: Conjectures and Counterexamples

This video tutorial explores the differences between inductive and deductive reasoning in mathematics. It defines both types of reasoning, provides examples, and explains how to classify arguments as either inductive or deductive. The video also discusses the use of counterexamples to disprove conjectures, emphasizing the importance of evidence in inductive reasoning and the necessity of conclusions in deductive reasoning.

What are the three main goals of the video?

• Use counterexamples, solve equations, and classify arguments.

• Define mathematical terms, solve equations, and use counterexamples.

• Classify arguments, solve problems, and define mathematical terms.

• Define inductive and deductive reasoning, classify arguments, and use counterexamples.

What type of reasoning uses patterns, trends, observations, and examples to make predictions?

• Inductive reasoning

• Mathematical reasoning

• Deductive reasoning

• Logical reasoning

In inductive reasoning, what do we call the predictions made based on gathered evidence?

• Hypotheses

• Proofs

• Theorems

• Conjectures

What type of reasoning starts with proven or accepted information and applies it to draw a necessary conclusion?

• Inductive reasoning

• Logical reasoning

• Deductive reasoning

• Empirical reasoning

In deductive reasoning, if all humans have hearts and Kim is a human, what can we conclude?

• Kim does not have a heart

• Kim has a heart

• Kim is not a human

• Kim is an animal

Which of the following is an example of inductive reasoning?

• All vegetables are purple; lettuce is a vegetable; therefore, lettuce is purple.

• The last six times we played our archrival in football, we won; therefore, we will win on Saturday.

• There is no mail delivery on holidays; tomorrow is Thanksgiving; therefore, my student loan check won't be delivered.

• All humans have hearts; Kim is a human; therefore, Kim has a heart.

Which of the following is an example of deductive reasoning?

• The last six times we played our archrival in football, we won; therefore, we will win on Saturday.

• I own an orange fish; my friend owns an orange fish; therefore, all fish are orange.

• We have seen many black crows; therefore, all crows are black.

• All vegetables are purple; lettuce is a vegetable; therefore, lettuce is purple.

What is the purpose of using counterexamples in reasoning?

• To make predictions

• To gather more evidence

• To prove a conjecture

• To disprove a conjecture

Which of the following is a counterexample to the conjecture that all fish are orange?

• A blue fish

• A green bird

• A cat that is not orange

• An orange fish

Which month can be used as a counterexample to the conjecture that the name of every month contains either the letter Y or the letter R?

• January

• March

• February

• June