# CLAST Math On-Line Practice Quiz

### (Chapter 5 - Form A: Logical Reasoning)

```  CLAST Logical Reasoning Skills

Deduce facts of set inclusion or set non-inclusion from a diagram
Identify negations of simple and compound statements
Determine equivalence and nonequivalence of statements
Draw logical conclusions from data
Recognize invalid arguments with true conclusions
Recognize valid reasoning patterns shown in everyday language
Select applicable rules for transforming statements without affecting their meaning
Draw logical conclusions when facts warrant them
```

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## Question 1

The negation of the statement "Bob is an engineer or Tom is a musician " is:

a) Bob is an engineer and Tom is not a musician.
b) Bob is not an engineer or Tom is not a musician.
c) Bob is not an engineer and Tom is a musician.
d) Bob is not an engineer and Tom is not a musician.

## Question 2

The negation of the statement "Pam is going to work and Kay is going shopping" is:

a) Pam is not going to work or Kay is going shopping.
b) Pam is going to work and Kay is not going shopping.
c) Pam is not going to work and Kay is not going shopping.
d) Pam is not going to work or Kay is not going shopping.

## Question 3

The negation of the statement "If Kari is offered a job, she will accept it" is:

a) If Kari is not offered a job, she will not accept it.
b) Kari is offered a job and she does not accept it.
c) Kari is offered a job and she accepts it.
d) If Kari is offered a job, she will not accept it.

## Question 4

The negation of the statement "All the employees will attend the picnic" is:

a) All the employees will not attend the picnic.
b) All the employees will attend the picnic.
c) Some employees will attend the picnic.
d) Some employees will not attend the picnic.

## Question 5

The statement logically equivalent to "It is not true that both Frank and Ralph are students" is:

a) Ralph is not a student and Frank is not a student.
b) If Frank is not a student, Ralph is not a student.
c) Frank is not a student or Ralph is not a student.
d) If Ralph is not a student, Frank is not a student.

## Question 6

The statement logically equivalent to "If Joe moves back east, then he will get homesick" is:

a) If Joe does not get homesick, then he moved back east.
b) Joe will get homesick, or he does not move back east.
c) Joe moves back east, or he does not get homesick.
d) Joe does not move back east or he does not get homesick.

## Question 7

The statement logically equivalent to "If Mary has a son, then she is a mother" is:

a) Mary has a son or she is a mother.
b) If Mary is a mother, then she has a son.
c) If Mary does not have a son, then she is not a mother.
d) If Mary is not a mother, then she does not have a son.

## Question 8

The statement NOT logically equivalent to "If the weather is warm, Wayne will go swimming" is:

a) Wayne will go swimming if the weather is warm.
b) If Wayne goes swimming, the weather is warm.
c) If Wayne does not go swimming, the weather is not warm.
d) The weather is not warm or Wayne will go swimming.

## Question 9

Select the rule of logical equivalence that directly transforms (in one step) statement "i" into statement "ii."

i.  If x2 is odd, then x is odd.
ii. If x is not odd, then x2 is not odd.

a) "If p, then q" is equivalent to "(not p) or q."
b) The correct equivalence rule is not given.
c) "Not (p and q)" is equivalent to "not p or not q."
d) "If p, then q" is equivalent to "if not q, then not p."

## Question 10

Select the rule of logical equivalence that directly transforms (in one step) statement "i" into statement "ii."

i.  Not all boys and girls are passing the class.
ii. Some boys or girls are not passing the class.

a) "If p then q" is equivalent to "if not q, then not p."
b) "Not (not p)" is equivalent to "p."
c) "All are not p" is equivalent to "none is p."
d) "Not all are p" is equivalent to "some are not p."

## Question 11

Sets A, B, C, and U are related as shown in the diagram below.

What statement can be made regarding the relationship among the sets, assuming none of the regions is empty?

a) Any element which is a member of set A and set B cannot be in set C.
b) No element which is a member of set C is also a member of set A.
c) All elements which are members of set A are also membes of set B.
d) Any element which is a member of set U is also a member of set C.

## Question 12

Given that :
i. No people who teach classes are dumb.
ii. All teachers teach classes.
Determine which conclusion can be logically deduced.

a) No teacher is dumb.
b) All teachers are dumb.
d) Some teachers are dumb.

## Question 13

Read the requirements and each applicant's qualifications for obtaining a \$25,000 loan, then identify which of the applicants would qualify for the loan.

To qualify for a loan of \$25,000 an applicant must have a gross income of \$15,000 if single (\$18,000 combined income if married) and assets of at least \$8,000.

Mr. Kerr is married with two children and makes \$19,000 on his job. His wife does not work.

Mrs. Mulvey and her husband have assets of \$12,000. One makes \$17,000; the other makes \$6,000.

Fred Stone is a bachelor and works at two jobs. He makes \$13,000 on one job and \$3,000 on the other; he also owns a \$7,000 Porsche.

a) Mrs. Mulvey
b) Mr. Kerr
c) No one
d) Fred Stone

## Question 14

Select the conclusion which will make the following argument valid.

If you graduate, then you will get a good job. If you get a good job, then you will be ecstatic.

a) If you graduate, then you will be ecstatic.
b) If you are ecstatic, then you graduated.
c) If you do not graduate, then you will not be ecstatic.
d) If you are not ecstatic, then you did not get a good job.

## Question 15

Study the information given below. If a logical conclusion is given, select that conclusion.

If you ask questions, you will learn a lot.
If you read often, you will learn a lot.

a) You will not learn a lot
c) You will learn a lot
d) You listen to others

## Question 16

Study the information given below. If a logical conclusion is given, select that conclusion.

All beachcombers are swimmers. All swimmers wear swimsuits.
Sally is wearing a swimsuit. Therefore:

a) Sally is a beachcomber
b) Sally cannot swim
c) Sally can swim

## Question 17

All of the following arguments A-D have true conclusions, but one of the arguments is not valid. Select the argument that is not valid.

a) All dogs have legs and all poodles are dogs.
Therefore, all poodles have legs.
b) All dogs bark and all poodles are dogs.
Therefore, all poodles bark.
c) All cats have two eyes and animals have two eyes.
Therefore, all cats are animals.
d) Every cat is an animal.
The tiger is a cat.
Therefore, the tiger is an animal

## Question 18

All of the following arguments A-D have true conclusions, but one of the arguments is not valid. Select the argument that is not valid.

a) Pam or Lois is a swimmer. Lois is not a swimmer.
Therefore, Pam is a swimmer.
b) Jane or Ann is a student. Jane is not a student.
Therefore, Ann is a student
c) Fred or James is a carpenter. Fred is a carpenter.
Therefore, Fred may be a carpenter.
d) Ryan or Al is going to the fair. Al is not going to the fair.
Therefore, Ryan is going to the fair.

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