2.2 Quick Check

What is a conjecture?

• a type of reasoning

• giving your opinion about a answer

• unproven statement based on observations

What is a counterexample?

• showing a conjecture is true

• showing a conjecture is false

What would be a counterexample to the statement:

Only boys have names that start with the letter T.

• Tom is a boy and his name starts with the letter T.

• Trish is a girl and her name starts with T.

Tags

CCSS.RI.8.1

CCSS.RI.8.8

CCSS.RL.8.1

CCSS.RL.9-10.1

CCSS.RL.7.1

What would be a counterexample to the statement:

All birds can fly.

• A parrot can fly.

• An ostrich cannot fly.

Tags

CCSS.RI.8.1

CCSS.RI.8.8

CCSS.RL.8.1

CCSS.RL.9-10.1

CCSS.RL.7.1

What is inductive reasoning?

• using a pattern to come up with a conjecture

• using your opinion to come up with a conjecture

• using definitions to come up with a conjecture

• using your imagination to come up with a conjecture

What is deductive reasoning?

• using a pattern to come up with a conjecture

• using your opinion to come up with a conjecture

• using facts to come up with a conjecture

• using your imagination to come up with a conjecture

Does the following use Inductive or Deductive reasoning?

Each time you forget to do your math homework, your parents take away your phone. So the next time you forget to do your math homework, you think you will lose your phone privileges.

• Inductive

• Deductive

Tags

CCSS.RI.8.1

CCSS.RI.8.8

CCSS.RL.8.1

CCSS.RL.9-10.1

CCSS.RI.7.8

Does the following use Inductive or Deductive reasoning?

Each time your mom goes to the store, she buys milk. So the next time your mom goes to the store, you expect her to buy milk.

• Deductive

• Inductive

Tags

CCSS.RI.8.1

CCSS.RI.8.8

CCSS.RL.8.1

CCSS.RL.9-10.1

CCSS.RL.11-12.1

Does the following use Inductive or Deductive reasoning?

Rational numbers can be written as a fraction. Irrational numbers cannot be written as a fraction. So  $\frac{1}{2}$  is a rational number.

• Deductive

• Inductive

Tags

CCSS.HSN.RN.B.3

Which uses the Law of Syllogism to make the conclusion?

(Hint: there is more than one answer)

• If I stay up late, then I will be tired.

  If am a tired, then I will fall asleep in class.

  If I stay up late, then I will fall asleep in class.

• If it is cold, then I wear a hat.

  If it is cold, then I wear gloves.

  I wear a hat and gloves when it is cold.

• If it is cold, then I wear a hat.

  Today is cold.

  I will wear a hat.

• If it rains, then I wear a raincoat.

  If I wear a raincoat, then I will sweat.

  If it rains, then I will sweat.