# 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 "Sarah is a fire fighter or Betty is a pro golfer" is:

a) Sarah is not a fire fighter and Betty is a pro golfer.
b) Sarh is a fire fighter and Betty is not a pro golfer.
c) Sarah is not a fire fighter and Betty is not a pro golfer.
d) Sarh is not a fire fighter or Betty is not a pro golfer.

## Question 2

The negation of the statement "Jim is going to work and Ann is going shopping" is:

a) Jim is not going to work or Ann is going shopping.
b) Jim is not going to work or Ann is not going shopping.
c) Jim is going to work and Ann is not going shopping.
d) Jim is not going to work and Ann is not going shopping.

## Question 3

The negation of the statement "If Janet receives an invitation, she will accept it" is:

a) Janet receives an invitation and she accepts it.
b) If Janet receives an invitation, she will not accept it.
c) Janet receives an invitation and she does not accept it.
d) If Janet does not receive an invitation, she will not accept it.

## Question 4

The negation of the statement "All the mothers are going to the banquet" is:

a) All the mothers are not going to the banquet.
b) Some mothers are going to the banquet.
c) Some mothers are not going to the banquet.
d) All the mothers are going to the banquet.

## Question 5

The statement logically equivalent to "It is not true that both Allen and Andrew are teachers" is:

a) If Allen is not a teacher, Andrew is not a teacher.
b) Andrew is not a teacher and Allen is not a teacher.
c) If Andrew is not a teacher, Allen is not a teacher.
d) Allen is not a teacher or Andrew is not a teacher.

## Question 6

The statement logically equivalent to "If Al fights with his brother, then he will get hurt" is:

a) Al does not fight with his brother or he does not get hurt.
b) Al fights with his brother, or he does not get hurt.
c) Al will get hurt, or he does not fight with his brother.
d) If Al does not get hurt, then he fights with his brother.

## Question 7

The statement logically equivalent to "If Sue is in Dallas, then she is in Texas" is:

a) If Sue is in Texas, then she is in Dallas.
b) Sue is in Dallas or she is in Texas.
c) If Sue is not in Dallas, then she is not in Texas.
d) If Sue is not in Texas, then she is not in Dallas.

## Question 8

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

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

## Question 9

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

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

a) The correct equivalence rule is not given.
b) "Not (p and q)" is equivalent to "not p or not q."
c) "If p, then q" is equivalent to "(not p) or 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 cats and dogs will be adopted.
ii. Some cat or dog will not be adopted.

a) "All are not p" is equivalent to "none is p."
b) "If p then q" is equivalent to "if not q, then not p."
c) "Not all are p" is equivalent to "some are not p."
d) "Not (not p)" is equivalent to "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) If an element is a member of set C, it may also be in set A or set B.
b) If an element is a member of set B, it is also a member of set A.
c) Any element that is a member of set A is also a member of set U.
d) If an element is a member of set A, it cannot be a member of set B.

## Question 12

Given that :
i. No people who run for office are reliable.
ii. All politicians run for office.
Determine which conclusion can be logically deduced.

a) All politicians are reliable.
c) Some politicians are reliable.
d) No politicians is reliable.

## Question 13

Read the requirements and each applicant's qualifications for obtaining a \$20,000 loan, then identify which of the applicants would qualify for the loan.

To qualify for a loan of \$20,000 an applicant must have a gross income of \$14,000 if single (\$17,000 combined income if married) and assets of at least \$7,000.

Mr. Jones is married with two children and makes \$12,000 on his job. His wife does not work.

Mrs. Via and her husband have assets of \$8,000. One makes \$12,000; the other makes \$4,000.

John Dawson is a bachelor and works at two jobs. He makes \$12,000 on one job and \$4,000 on the other; he also owns a \$8,000 Porsche.

a) John Dawson
b) No one
c) Mrs. Via
d) Mr. Jones

## Question 14

Select the conclusion which will make the following argument valid.

If you work hard, then you will get a good job. If you get a good job, then you will be well paid.

a) If you do not work hard, then you will not be well paid.
b) If you are well paid, then you worked hard.
c) If you are not well paid, then you did not get a good job.
d) If you work hard, then you will be well paid.

## Question 15

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

If you study mathematics, you will be successful.
If you study English, you will be successful.
You study English and not Mathematics. Therefore:

a) You will not be successful
c) You study French also
d) You will be successful

## Question 16

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

All pilots are navigators. All navigators read maps.
Sally is reading a map. Therefore:

a) Sally cannot navigate
b) Sally is a pilot
d) Sally can navigate

## 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 birds have feathers and all penguins are birds.
Therefore, all penguins have feathers.
b) All fleas have six legs and insects have six legs.
Therefore, all fleas are insects.
c) All birds have legs and all penguins are birds.
Therefore, all penguins have legs.
d) Every borough of New York City is in New York State.
The Bronx is a borough of New York City.
Therefore, the Bronx is in New York State.

## 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) Fred or James is a carpenter. Fred is a carpenter.
Therefore, Fred may be a carpenter.
b) Jane or Ann is a student. Jane is not a student.
Therefore, Ann is a student
c) Pam or Lois is a swimmer. Lois is not a swimmer.
Therefore, Pam is a swimmer.
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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