Free Printable 3.2-3.4 Review Game

1.

p: It is raining.

q: The game is cancelled.

It is not raining and the game is cancelled.

a)

$p\rightarrow q$

b)

$q\rightarrow p$

c)

$\sim p\rightarrow q$

d)

$\sim p\wedge q$

2.

Let p represent: Luis watches TV.

Let q represent: Luis goes on a walk.

Translate the verbal argument into symbolic form.

Therefore, Luis does not go on a walk.

a)

$\therefore q$

b)

$\therefore\sim q$

c)

$q$

d)

$\sim q$

3.

Let a represent: Mariela plays basketball.

Let b represent: Mariela sings.

Let c represent: Mariela takes photos.

Convert the following verbal statement into the correct symbolic notation.

Mariela plays basketball or she takes photos.

a)

$a\ \wedge\ c$

b)

$a\ \vee\ c$

c)

$b\ \vee\ c$

d)

$a\ \wedge\ b$

4.

p: It is raining.

q: The game is cancelled.

r: The boy is sad.

If it is raining and the game is cancelled, then the boy is sad.

a)

$p\rightarrow q\wedge r$

b)

$q\rightarrow p\vee r$

c)

$p\wedge q\rightarrow r$

d)

$\sim p\wedge q\vee r$

5.

p: It is raining.

q: The game is cancelled.

r: The boy is sad.

The game is cancelled and the boy is sad; therefore, it is raining.

a)

$q\wedge r\therefore p$

b)

$q\vee r\therefore p$

c)

$q\rightarrow r\wedge p$

d)

$q\wedge\sim r\rightarrow p$

6.

g: The girl runs.
h: The rabbit hops.
j: The girl and the rabbit are having fun.

\sim g\vee\sim h\rightarrow\sim j

a)

If the girl runs or the rabbit doesn't hop, then they are having fun.

b)

If the girl doesn't run or the rabbit doesn't hop, then they are not having fun.

c)

If the girl runs and the rabbit hops, then they are having fun,

d)

If the girl doesn't run and the rabbit doesn't hop, then they are not having fun.

7.

Translate the symbolic notation to a verbal expression.

Let p represent: Ms. Keesling bought new sneakers.
Let q represent: The students like Ms. Keesling's shoes.
Let s represent: Ms. Keesling is sad.

$p\ \wedge\sim q\therefore s$

a)

Ms. Keesling didn't buy new sneakers therefore she is sad.

b)

Ms. Keesling bought new sneakers or the students didn't like Ms. Keesling's shoes, so she is sad.

c)

Ms. Keesling bought new sneakers and the students didn't like Ms. Keesling's shoes, therefore Ms. Keesling is sad.

d)

If Ms. Keesling bought new sneakers and the students didn't like Ms. Keesling's shoes, then she is sad.

8.

Translate the symbolic notation to a verbal expression.

Let p represent: There is a quiz today.
Let q represent: The students feel prepared.
Let s represent: Ms. Keesling is happy.

$p\ \wedge\ q\ \longrightarrow\ s$

a)

There is a quiz today and the students don't feel prepared therefore Ms. Keesling is happy.

b)

If there is a quiz today and the students feel prepared, then Ms. Keesling is happy.

c)

If there is a quiz today and the students don't feel prepared then Ms. Keesling is happy.

d)

Ms. Keesling is happy therefore there is a quiz today or the students feel prepared.

9.

Translate the symbolic notation to a verbal expression.

Let p represent: There is a quiz today.
Let q represent: The students feel prepared.
Let s represent: Ms. Keesling is happy.
Let t represent: The students are happy.
$p\ \wedge\ q\ \therefore\ s\ \wedge\ t$

a)

There is a quiz today and the students feel prepared therefore Ms. Keesling and the students are happy

b)

If there is a quiz today and the students feel prepared, then Ms. Keesling and the students are happy.

c)

There is not a quiz today or the students feel prepared then Ms. Keesling or the students are happy.

d)

There is a quiz today and the students feel prepared or Ms. Keesling and the students are happy.

10.

Translate the symbolic notation to a verbal expression.

Let p represent: There is a quiz today.
Let q represent: The students feel prepared.
Let s represent: Ms. Keesling is happy.
Let t represent: The students are happy.
$p\ \wedge\ \sim q\ \longrightarrow\ \sim s\ \wedge\ \sim t$

a)

There is a quiz today and the students don't feel prepared therefore Ms. Keesling and the students are not happy

b)

If there is a quiz today and the students feel prepared, then Ms. Keesling and the students are happy.

c)

There is not a quiz today and the students feel prepared then Ms. Keesling or the students are happy.

d)

If there is a quiz today and the student's don't feel prepared then Ms. Keesling and the students are not happy.

11.

If it is a number, then it is either positive or negative.

What is an appropriate counterexample?

a)

10

b)

-2

c)

0

d)

True. There is no counterexample.

12.

Which of these is a counterexample to the following statement?

All vegetables are green.

a)

Banana

b)

Pumpkins

c)

Green Beans

d)

Grass

13.

If it is an angle, then it is acute. What is an appropriate counterexample?

a)

70⁰

b)

45⁰

c)

120⁰

d)

True. There is no counterexample.

14.

Which of the following is a counterexample for this conditional statement:

If a playing card from a standard deck is red, then it is a heart.

a)

a spade

b)

a diamond

c)

a heart

d)

a club

15.

The product of two negative numbers is greater than the sum of the two numbers. What is an appropriate counterexample?

a)

-3 and -3

b)

True. There is no counterexample

c)

-1 and -1

d)

4 and 6

16.

What is a counterexample to the statement: "A triangle can be drawn from any 3 points"?

a)

The 3 points all lie on a circle

b)

The 3 points lie on separate lines

c)

The 3 points form a quadrilateral

d)

The 3 points are colinear

17.

How many counterexamples do you need to prove that an argument is invalid?

a)

0

b)

1

c)

2

d)

All possible counterexamples

18.

Decide if the statement is true or false. If the statement is false, provide a counterexample.

If I go to WBHS, then I am a 10th grader.

a)

I am a 10th grader

b)

True. There are no counterexamples.

c)

I am a senior

d)

I don't go to WBHS

19.

Decide if the following conjecture is true or false. If it is false, provide a counterexample.

All even numbers are divisible by 2.

a)

7

b)

44

c)

18

d)

True. There are no counterexamples.

20.

Decide if the following conjecture is true or false. If false, select a counterexample.

All people have hair.

a)

My hair is blonde.

b)

Some people are bald.

c)

I am not a person.

d)

Hairless cats

21.

In order to write a biconditional, what two things need to be true?

a)

The conditional and the inverse.

b)

The conditional and the converse.

c)

The conditional and the contrapositive.

d)

The converse and the inverse

22.

What counterexample makes the following biconditional false?

"It is Halloween if and only if it is October 31."

a)

This is a true biconditional, so it has no counterexamples.

b)

It is not October 31.

c)

I don't celebrate Halloween.

d)

It is October 30.

23.

"If you live in Vinton, then you live in Virginia."

Would the biconditional be ....?

a)

TRUE - Vinton is in Virginia.

b)

TRUE - The converse is also true.

c)

FALSE - You can live in Virginia, but somewhere other than Vinton.

d)

FALSE - There is no where else to live besides Vinton.

24.

What is the biconditional that matches the statement: "A right angle is an angle with 90 degrees."

a)

If an angle has 90 degrees, then it is a right angle.

b)

If an angle is a right angle, then it has 90 degrees.

c)

An angle is a right angle if and only if it has 90 degrees.

25.

What is the biconditional that matches the statement below: An even number is a number that is divisible by 2.

a)

A number is even if and only if it is divisible by 2.

b)

If a number is divisible by 2, then it is even.

c)

If a number is even, then it is divisible by 2.

26.

Select the conditional statement of the biconditional statement:

I am a junior if and only if I am in 11th grade.

a)

I am a junior

b)

If I am a junior, then I am in 11th grade.

c)

I am in 11th grade

27.

Write the conditional statements as a biconditional statement:

1) If B is between A and C, then AB+BC=AC.

2) If AB+BC=AC, then B is between A and C.

a)

Segment Addition Postulate

b)

B is between A and C when AB+BC=AC if and only if Segment Addition Postulate.

c)

B is between A and C if and only if AB+BC=AC.

28.

Select the conditional statement(s) of the biconditional statement:

Points lie in one plane if and only if they are coplanar.

a)

Coplanar points lie in one plane.

b)

If points lie in one plane, then they are coplanar.

c)

If points are coplanar, then they lie in one plane.

d)

Planes have coplanar points.

29.

What is the truth value of the converse of:

"If a number is divisible by 20, then it is even."

a)

True

b)

False

c)

Cannot be determined

30.

Test the statement below to see if it is reversible. If so, write it as a biconditional.

Complementary angles are two angles with measures that have a sum of 90.

a)

Reversible; If two angles are complementary, then the sum of their measures is 90.

b)

Reversible; Two angles are complementary if and only if the sum of their measures is 90.

c)

Not reversible.

3.2-3.4 Review Game

Total questions: 30

Worksheet time: 49mins

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