Unit 2 Reasoning Review

Conditional/Converse

100

Write a conditional statement: Tenth graders are in Geometry.

"If you are a tenth grader, then you are in Geometry."

200

Write a conditional statement: Puppies are small.

"If it is a puppy, then it is small"

300

Write a conditional statement: A line contains at least 2 points.

"If it is a line, then it contains at least 2 points."

400

Write the converse of the following conditional statement: If x is positive, then 2x is larger than x.

"If 2x is larger than x, then x is a positive."

500

Write the converse of the following conditional statement: If a plane contains exactly three points, then they are non-collinear.

"If three points are non-collinear, then they are a plane."

Inductive vs. Deductive

100

Answer inductive or deductive reasoning. Johnny is a bachelor. All bachelors are single. Therefore, Johnny is single.

Deductive Reasoning

200

Answer inductive or deductive reasoning. Jennifer leaves for school at 7 am and is on time. Therefore, if Jennifer leaves for school at 7 am she will always be on time.

Inductive Reasoning

300

Answer inductive or deductive reasoning. All the swans we have seen are white; therefore, all swans are white.

Inductive Reasoning

400

Answer inductive or deductive and give the answer. My dog runs 25 mph. I run 14 mph. What can be concluded?

Deductive Reasoning, my dog can run faster than me.

500

Answer inductive or deductive and give the answer. Mary and Sue are friends. Mary enjoys fishing, running and rock climbing. Sue likes fishing and running.

Inductive Reasoning, she must also like rock climbing.

Contrapositive

100

If you like tennis, then you play on the tennis team.

"If you do not play on the tennis team, then you do not like tennis"

200

If x is odd, then 2x is even.

"If 2x is not even, then x is not odd."

300

If a point lies on 2 lines, then it is at the intersection.

"If a point is not at the intersection, then it does not lie on 2 lines."

400

If you like purple, then you love Barney.

"If you do not love Barney, then you do not like purple."

500

What is the mathematical notation for the contrapositive? (Hint: A regular conditional is noted p --> q)

~q --> ~p

Inverse

100

If x is odd, then 3x is odd.

"If x is not odd, then 3x is not odd"

200

If you like hockey, then you will go to the hockey game.

"If you do not like hockey, then you will not go to the hockey game."

300

If you visited the White House, then you've been to Washington D.C.

"If you have not visited the White House, then you have not been to Washington D.C."

400

If you are 16, then you can legally drive. Is the inverse of this statement true or false, and why?

"If you are not 16, then you can not legally drive." FALSE - those older than 16 can also legally drive

500

What is the mathematical notation for inverse? (Hint: The regular conditional is notated p --> q)

~p --> ~q