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Review Math 1001 Test #1 (1.1,1.2,3.1-3.6,2.1-2.3)

Total questions: 61

Worksheet time: 2hrs 36mins

Name
Class
Date
1.
What are the missing numbers in this pattern?
23, 33, ___, 53, ___, 73
a)
32, 62
b)
42, 63
c)
43, 63
d)
42, 62
2.
Which number is a counterexample to the following statement? : 
All numbers that are divisible by 2 are divisible by 4
a)
0
b)
12
c)
28
d)
42
3.

What are the next 3 terms in the following geometric sequence:

512, 256, 128, ___, ___, ___, ...

a)

1024, 2048, 4096

b)

32, 8, 2

c)

64, 32, 16

d)

92, 66, 38

4.
Determine whether the sequence is arithmetic, geometric, or neither.
a)
arithmetic
b)
geometric
c)
neither
5.
Determine whether the sequence is arithmetic, geometric, or neither.
a)
arithmetic
b)
geometric
c)
neither
6.

Which is a counterexample to the following statement?


If you add two numbers, then the sum is always odd.

a)

2+5=7

b)

3+2=5

c)

1+8=9

d)

2+4=6

7.
Snakes are reptiles and reptiles are cold blooded; therefore, snakes are cold blooded. 
a)
Deductive
b)
Inductive 
8.
All observed houses on South Street have roofs that are falling apart.  Sherry lives on South Street.  Her roof is falling apart. 
a)
Deductive
b)
Inductive
9.

Is Inductive or Deductive reasoning used in this situation?


The catalog states that all incoming freshman must take the math placement exam.

You are an entering freshman.

Therefore you must take the math placement exam.

a)

Inductive

b)

Deductive

10.

In the past, winter has always been cold in Loei. Therefore, winter will be cold again this year.

a)

Deductive

b)

Inductive

11.
Given, "If I have a Siberian Husky, then I have a dog." Identify the inverse.
a)
If I do not have a Siberian Husky, then I do not have a dog.
b)
If I have a dog, then I have a Siberian Husky.
c)
If I do not have a dog, then I do not have a Siberian Husky.
d)
If I do not have a Siberian Husky, then I have a dog. 
12.
Given, "If I have a Siberian Husky, then I have a dog." Identify the contrapositive.
a)
If I do not have a Siberian Husky, then I do not have a dog.
b)
If I have a dog, then I have a Siberian Husky.
c)
If I do not have a dog, then I do not have a Siberian Husky.
d)
If I do not have a Siberian Husky, then I have a dog. 
13.
This symbol, ∨, means?
a)
and
b)
or
c)
not
d)
implies
14.
This symbol, ∧, means?
a)
and
b)
or 
c)
not 
d)
implies
15.
This symbol, ↔, means?
a)
and
b)
or 
c)
if and only if
d)
implies
16.

p represents "Brent works this summer"

q represents "Brent takes a vacation"

Which symbols best represent the statement: "If Brent works this summer then he will not take a vacation." ?

a)

p → q

b)

q→ p

c)

p → ~q

d)

~p → ~q

17.

r:  it is raining

s: sidewalks are wet

Write the statement: "If it is not raining then the sidewalks are not wet" in symbolic form.

a)
∼r→∼s
b)
∼s→r
c)
r→s
d)
s→r
18.

Use a truth table to determine if the statement is a tautology, self-contradiction, or neither. [(p →\rightarrow  q) ∧\wedge ~q] →\rightarrow  ~p

a)

neither

b)

tautology

c)

self-contradiction

19.

p: the wind is blowing

q: the air is hazy

r: the weather is dry

Which of the following represents:

"If the wind is blowing, then the air is hazy or the weather is dry"

a)

p /\ (q V r)

b)

p → (r /\ q)

c)

p /\ (q /\ r)

d)

p → (q V r)

20.

Translate the following argument into symbols.  Choose the correct answer below.

If the bus is on time, I will get to class on time.  I got to class on time.  Therefore, the bus was on time.

a)

(p ∧ q) ∨ p ⇒ q 

b)

(p → q) ∧ q ⇒ p 

c)

(p → q) ∨ q ⇒ p 

d)

(p ∧ q) ∧ p ⇒ q

21.

Translate the following argument into symbols.  Choose the correct answer below.

Either this milk has expired, or I am sick. The milk hasn’t expired. Therefore, I must be sick.

a)

(~p ∧ q) ∨ p ⇒ q   

b)

(p → ~q) ∨ q ⇒ ~p 

c)

(p ∨ q) ∧ ~p ⇒ q 

d)

(p → q) ∧ ~p ⇒ ~q 

22.

Which of the following is a statement?

a)

Let’s play in the field.

b)

Is 3 + 2 = 8?

c)

– 6 < –8.

d)

I love pizza.

23.

Choose a negation for the following statement :

41 is a prime number.

a)

One of the prime numbers is 41.

b)

41 is not a prime number.

c)

41 is an odd number.

d)

41 is not an even number.

24.

Determine which one is a statement.

a)

Go home!

b)

A prime number has 2 factors.

c)

χ + γ

d)

Express 2300 in standard form.

e)

Money is the root of all evil.

25.

What is the symbol for Negation?

a)

∕

b)

∨

c)

~

d)

∧

26.

Select the negation of this statement:

The Earth is round in shape.

a)

Venus is round in shape.

b)

The round Earth is not a shape.

c)

The Earth is square in shape.

d)

The Earth is not round in shape.

27.

Is the argument represented in this truth table valid or invalid?

HINT: Complete the Truth Table. Use the completed Truth Table to answer the question.

a)

Valid

b)

Invalid

28.

Which statement is the converse of the given statement?

"If you make an insurance claim, then your rates will go up."

a)

If your insurance rates do not go up , then you have not made a claim.

b)
If you do not make an insurance claim, then your rates will not go up.
c)
If your insurance rates go up, then you have made an insurance claim.
d)
If you make an insurance claim, then your rates will not go up.
29.

What type of logic is this table showing:

a)

AND

b)

OR

c)

NOT

d)

If Then

30.

Find the final column of the truth table for

~(q →\rightarrow  p).

a)

FFTF

b)

TTFF

c)

FFFF

d)

TTFT

31.

What are the truth values for ~p ∨ q

a)

T F T T

b)

T T F T

c)

T T T F

d)

F T T T

32.

What are the truth values for (p ∧ q) → ~q

a)

F F F F

b)

F T T T

c)

T T T F

d)

T T F T

33.

p: the wind is blowing


q: the air is hazy


r: the weather is dry


The symbolic statement r ----> (p v ~q)


Is written as a worded statement:

a)

if the weather is dry then, the air is not hazy and the weather is not dry

b)

if the wind is blowing then, the air is hazy or the weather is not dry

c)

if the weather is dry then, the wind is blowing or the air is not hazy

d)

the weather is dry if and only if, the air is hazy or the wind is not blowing

34.

Use a truth table to determine if the following statements are logically equivalent, negations or neither.

Statement #1: ~(p -> q)

Statement #2: ~p -> ~q

a)

neither

b)

logically equivalent

c)

negations

35.

Use a truth table to determine if the following statements are logically equivalent, negations or neither.

Statement #1: p -> q

Statement #2: ~q -> ~p

a)

neither

b)

logically equivalent

c)

negations

36.

State whether the argument below is valid or invalid.

If Joe eats greasy food, he will feel sick.

Joe does not feel sick.

Therefore, Joe did not eat greasy food.

a)

valid

b)

invalid

37.

If I go camping, then I need to pack my tent.

I packed my tent.

Therefore, I went camping.

Valid or Invalid argument?

a)

Valid

b)

Invalid

38.

Round 23.456 to the nearest hundredth

a)

24.00

b)

23.45

c)

23.46

d)

23.40

39.
What is 245 rounded to the nearest hundred?
a)
250
b)
240
c)
300
d)
200
40.
Round 45,291 to the tens place.
a)

45,300

b)
45,200
c)
45,290
d)
46,000
41.

Find the n(A) if A = {x, y, z, w}

a)

3

b)

2

c)

1

d)

4

42.

What does this symbol mean?

∉

a)

Is not a member of

b)

Is not an intersection

c)

Not the universal set

d)

Empty set

43.

What does this symbol mean?

⊂

a)

Subset

b)

Union

c)

Intersection

d)

Proper Subset

44.
Given that
set  V = { m, n, o, p },
find the number of subsets  V.
a)
16
b)
12
c)
10
d)
8
45.
Set  Q  contains the letters in the word  SISTER .
 Which of the following is set  Q ?
a)
Q = { S, T, R }
b)
Q = { I, E }
c)
Q = { S, I, S, T, E, R }
d)
Q = { S, I, T, E, R }
46.

Determine if the sets are equal, equivalent, both or neither: { man, woman, girl, boy } and { 10, 20, 30, 40}

a)

Equal

b)

Equivalent

c)

Both

d)

Neither

47.

A = { John, Peter, James, Jude}

C = {Hamed, John, Ali, Jude}


find A ∩ C

a)

{John, Peter, James, Jude, Hamed, Ali}

b)

{James}

c)

{Hamed, James}

d)

{John, Jude}

48.

If U = { red, blue, green, yellow, purple} and

A = {red, blue,yellow},

what is A', the complement of set A?

a)

A' = {green, purple}

b)

A' = {purple}

c)

A' = {blue, red, purple}

d)

A' = {red, blue green}

49.

Given the sets
A = {2, 3, 4, 5} and B = {2, 4, 5, 6}

What is A ∪ B  ?

a)

{2, 4, 5}

b)

{2, 3, 4, 5, 6}

c)

{3}

d)

{6}

50.

If A = {1, 2, 3, 4, 5, 6}, B = {1, 2, 3, 5, 7, 9} and C = {3, 5, 6, 7, 8, 9}


What is (A ⋃ B) ⋂ C?

a)

{3, 4, 5, 6, 7, 9}

b)

{3, 4, 5, 6, 7, 8, 9}

c)

{3, 5, 6, 7, 9}

d)

{ }

51.
Determine if the statement is true or false.
{10, 12, 14, 16} ⊆ {1,2,3,4,...99}
a)
True
b)
False
52.

Fill in the blank with the best choice.
13 ____ {1,2,3,4,..., 20}

a)

⊂\subset

b)

∈\in

c)

⊆\subseteq

d)

⟶\longrightarrow

53.

Given the sets

U = {1, 2, 3, 4, 5, 6, 7, 8, 9}

A = {2, 3, 5, 7} and B = {1, 3, 5, 7, 9}


What is (A∪B)′ ?

a)

{1, 2, 3, 5, 7, 9}

b)

{4, 6, 8}

c)

{2, 4, 6, 8}

d)

{1, 3, 5, 7, 9}

54.

Let A={1, 3, 4} and B={x|x is an even whole number less than 9}. Find A ∩ B

a)

{1, 3, 4}

b)

{1, 2, 3, 4, 6, 8}

c)

{4}

d)

{ }

55.

What type of set is denoted as either { } or ∅?

a)

Superset

b)

Disjointed Set

c)

Empty (or Null) Set

d)

Subset

56.

What is the cardinal number of the set,

H = {w, o, n, d, e, r, f, u, l} ?

a)

10

b)

9

c)

7

d)

8

57.

Set C is the set of natural numbers less than 9. Write the set using the Roster method.

a)

C = {1, 2, 3, 4, 5, 6, 7, 8, 9}

b)

C = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

c)

C = {2, 4, 6, 8}

d)

C = {1, 2, 3, 4, 5, 6, 7, 8}

58.

Which of the following is true?

(Note: there may be more than one answer)

a)

The cardinality of an empty set is 1.

b)

If two sets have exactly the same elements, then they are equal.

c)

If two sets are equal, then they are equivalent.

d)

If two sets are equivalent, then they are equal.

59.

Every set has _____ as one of its subsets (select all that apply.)

a)

itself

b)

∅

c)

0

d)

real numbers

60.

Which of these is something both whales and fish have in common?

a)

live birth

b)

lay eggs

c)

have fins

d)

have hair

61.

Which important fact is about Abraham Lincoln, but not John F. Kennedy?

a)

Born in Kentucky

b)

former President of the United States

c)

Democratic Party

d)

Born May 29

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