Reasoning & Proof

Lesson 2.1-2.3 Review

Multiple Choice

What is the next number in the pattern? 5, 10, 15, 20...

• 15

• 25

• 30

• 40

Multiple Choice

What is the next number in the pattern? 2, 6, 18, 54...

• 108

• 98

• 156

• 162

Multiple Select

What is a counter example to the following statement?

"Any four-sided polygon is a square"

• A square has four congruent sides.

• There are four equal angles in a square.

• A trapezoid has four sides and is a polygon.

• A triangle is a polygon.

Multiple Choice

Write the statement in if-then form:

"You have a fever if your body temperature is 103 degrees."

• If you are sick then you have a fever.

• If you have a fever then your body temperature is 103 degrees.

• if you don't feel well then you will have a fever.

• If someone has a fever then they might be sick.

Multiple Choice

What is a converse statement?

• When you flip the hypothesis and conclusion.

• When write someone in if-then form.

• When you negate the hypothesis and conclusion.

• When you flip and negate the hypothesis and conclusion.

Multiple Choice

What is an inverse statement?

• When you write something in if-then form.

• When you flip the hypothesis and the conclusion.

• When you negate the hypothesis and the conclusion.

• When you flip and negate the hypothesis and conclusion.

Multiple Choice

What is a contrapositive statement?

• When you write something in if-then form.

• When you flip the hypothesis and the conclusion.

• When you negate the hypothesis and the conclusion.

• When you flip and negate the hypothesis and the conclusion.

Multiple Choice

Use the law of detachment to make a valid conclusion.

"If you get a hit, then your baseball team will win. You hit a home run."

• Your team loses the game.

• Your team wins the game.

• You strike out.

• You have a team party.

Multiple Choice

Use the law of detachment to make a valid conclusion.

"f Rylee gets promoted, then Callie will also be promoted. Rylee is promoted"

• Rylee gets fired.

• They both quit.

• Callie quits her job.

• Callie gets promoted.

Multiple Choice

Use the law of syllogism to find the next statement:

"If you mail the payment by noon, then it will arrive by tomorrow. If your payment arrives by tomorrow, then you won’t be charged a late fee."

• If you mail the payment by noon, then you won't be charged a late fee.

• If you won't be charged a late fee, then you mail the payment by noon.

• It will arrive by tomorrow.

Multiple Choice

Use the law of syllogism to find the next statement:

"If a triangle has two angles of 60 degrees, then the triangle is equiangular. If a triangle is equiangular, then it is also equilateral."

• The triangle is equiangular.

• If a triangle has two angles of 60 degrees, then it is also equilateral.

• It is equilateral, if it is equiangular.

Multiple Choice

Decide whether the conclusion reached from the two statements demonstrates the Law of Detachment, the Law of Syllogism, or neither.

"If Cedric plays in a big game, then he gets nervous. If Cedric gets nervous, then he performs well.

Conclusion: If Cedric plays in a big game, then he performs well."

• Law of Detachment

• Law of Syllogism

• neither

Multiple Choice

Decide whether the conclusion reached from the two statements demonstrates the Law of Detachment, the Law of Syllogism, or neither.

"If Leanne spends more than $30 on her car, then she’ll have to wait until next week to buy Michael’s birthday gift. Leanne spent $40 on her car.

Conclusion: Leanne will have to wait until next week to buy Michael’s birthday gift."

• Law of Detachment

• Law of Syllogism

• neither

Multiple Choice

Decide whether the conclusion reached from the two statements demonstrates the Law of Detachment, the Law of Syllogism, or neither.

"If Lavonne gets money, she gives half of it to Sid. If Sid gets money, he gives half of it to Lavonne.

Conclusion: Lavonne and Sid share their money equally."

• Law of Detachment

• Law of Syllogism

• neither

Multiple Choice

Decide whether inductive or deductive reasoning is used to reach the conclusion.

"While shopping for a product, you notice that brand A is more expensive than brand B. You conclude that brand A is of higher quality than brand B."

• inductive reasoning

• deductive reasoning

Multiple Choice

Decide whether inductive or deductive reasoning is used to reach the conclusion.

"Because the brand A product costs $1.50 and the brand B product costs $1.00, you conclude that the brand A product is 50% more expensive."

• Inductive Reasoning

• Deductive Reasoning