Free Printable EdMath 301 - Long Quiz

1.

_________ is the symbol for "the set of all integers."

a)

Z

b)

Q

c)

R

d)

C

2.

_________ is the symbol for "the set of all rational numbers."

a)

Z

b)

Q

c)

R

d)

C

3.

_________ is the symbol for "set of all real numbers"

a)

Z

b)

Q

c)

R

d)

C

4.

________ is the symbol for "the set of all complex numbers."

a)

Z

b)

Q

c)

R

d)

C

5.

A set with only one member is called ______________.

a)

singleton set

b)

element

c)

power set

d)

null set

6.

A way of specifying a set by listing all its members.

a)

List Notation

b)

Predicate Notation

c)

Set-builder notation

d)

Recursive rules

7.

Specifying a set by stating a property of its elements.

a)

List Notation

b)

Predicate Notation

c)

Property of a set

d)

Recursive Rules

8.

Specifying a set by defining a set of rules which generates (defines) its

members.

a)

List Notation

b)

Set-Builder Notation

c)

Set Definition

d)

Recursive rules

9.

{1, 12, 45},

{George Washington, Bill Clinton},

{a,b,d,m},

{1,2,...,100}

These sets are specified in the form of ___________.

a)

List notation

b)

Predicate notation

c)

Set-builder notation

d)

Recursive rules

10.

{x I x is a natural number and x<8}

a)

List Notation

b)

Precate Notation

c)

Recursive Rules

d)

Set-Builder Notation

11.

Which of the following is TRUE with the given set?

"the set E of even numbers greater than 3"

a)

$4\ \in\ E$

b)

$2\ \in\ E$

c)

$5\ \in\ E$

d)

$\ -4\in\ E$

12.

Two

sets are IDENTICAL if and only if they have exactly the

SAME MEMBERS

a)

$A=B$ iff for every x, $x\in A\Longleftrightarrow x\in B$

b)

$A=B$ iff for every x, $x\in A\cup B$

c)

$A=B$ iff for every x, $x\in A\cap B$

d)

$A=B$ iff for every x, $x\in AB$

13.

The cardinality of a FINITE SET is _____________

a)

a natural number

b)

not a natural number

c)

a rational number

d)

zero

14.

INFINITE SETS also have cardinalities but they are ________.

a)

not natural numbers

b)

natural numbers

c)

elements

d)

sets

15.

A set A is a subset of a set B iff every element of A is _____________.

a)

also an

element of B

b)

$A\ne B$

c)

$\notin B$

d)

not an element of B.

16.

If $A\subseteq B$ and

$A\ne B$ , we call A ____________.

a)

Singleton Set

b)

Proper Set

c)

Proper Subset

d)

Null Set

17.

Which of the following is NOT TRUE about subsets and proper subsets?

a)

$\left\{a,b\right\}\subseteq\left\{d,a,b,e\right\}$

b)

$\left\{a,b\right\}\subset\left\{d,a,b,e\right\}$

c)

{a,b} is a subset of {a,b}

d)

{a,b} is a proper subset of {a,b}

18.

The set of all subsets of a set A is called _____________.

a)

Power set of A

b)

Null Set

c)

Subset of A

d)

Cardinality

19.

If $A=\left\{a,b\right\}$ , then its power set is ___________.

a)

null set

b)

{null set, {a}, {b}}

c)

{null set, {a}, {b}, {ab}}

d)

{null set, {a}, {b}, {a,b}}

20.

The UNION of A and B is ________________________.

a)

$A\cap B$

b)

x in A and B

c)

the set whose elements

are just the elements of A or B

d)

the set whose elements

are just the elements of A and B

21.

The INTERSECTION of A and B is _____________________.

a)

$A\cup B$

b)

is the set whose

elements are just the elements of both A and B

c)

is the set whose

elements are just the elements of both A or B

d)

A - B

22.

If K = {a,b}, L= {c,d}, and M = {b,d}, then

a)

$K\cap L=\phi$

b)

$K\cap M=\left\{a,b,d\right\}$

c)

$L\cap M=\left\{c,b\right\}$

d)

$K\cup L\cup M=\left\{a,b,c,d,e\right\}$

23.

$A-B=\left\{x\parallel x\in A\ and\ x\notin B\right\}$

a)

Union

b)

Intersection

c)

Complement of B relative to A

d)

Complement of A relative to B

24.

$A\cup B\ =\ \left\{x\parallel x\in A\ or\ x\in B\right\}$

a)

Union

b)

Intersection

c)

Subset

d)

Proper Subset

25.

$A\cap B\ =\ \left\{x\parallel x\in A\ and\ x\in B\right\}$

a)

Union

b)

Intersection

c)

Subset

d)

Proper Subset

26.

Which of the following is NOT TRUE about $A'\ =\ \left\{x\parallel x\notin A\right\}$ ?

a)

Set consisting of everything not in A

b)

$A'\ =\ U-A$

c)

$A'\ =\ A-U$

d)

the complement of A is equal to universal set minus A.

27.

Idempotent Laws

a)

$X\cup X=X$

b)

$X\cup Y=Y\cup X$

c)

$X\cup\phi=X$

d)

$X\cup X'=U$

28.

Commutative Laws

a)

$X\cup X=X$

b)

$X\cup Y=Y\cup X$

c)

$X\cup\phi=X$

d)

$X\cup X'=U$

29.

Identity Laws

a)

$X\cup X=X$

b)

$X\cup Y=Y\cup X$

c)

$X\cup\phi=X$

d)

$X\cup X'=U$

30.

Complement Laws

a)

$X\cup X=X$

b)

$X\cup Y=Y\cup X$

c)

$X\cup\phi=X$

d)

$X\cup X'=U$

31.

Associative Laws

a)

$\left(X\cup Y\right)\cup Z\ =\ X\cup\left(Y\cup Z\right)\$

b)

$X\cup\left(Y\cap Z\right)\ =\ \left(X\cup Y\right)\cap\left(X\cup Z\right)$

c)

$\left(X\cup Y\right)'\ =\ X'\ \cap Y'$

d)

$X\subseteq Y\ \ \ iff\ \ X\cup Y=Y$

32.

Distributive Laws

a)

$\left(X\cup Y\right)\cup Z\ =\ X\cup\left(Y\cup Z\right)\$

b)

$X\cup\left(Y\cap Z\right)\ =\ \left(X\cup Y\right)\cap\left(X\cup Z\right)$

c)

$\left(X\cup Y\right)'\ =\ X'\ \cap Y'$

d)

$X\subseteq Y\ \ \ iff\ \ X\cup Y=Y$

33.

DeMorgan's Laws

a)

$\left(X\cup Y\right)\cup Z\ =\ X\cup\left(Y\cup Z\right)\$

b)

$X\cup\left(Y\cap Z\right)\ =\ \left(X\cup Y\right)\cap\left(X\cup Z\right)$

c)

$\left(X\cup Y\right)'\ =\ X'\ \cap Y'$

d)

$X\subseteq Y\ \ \ iff\ \ X\cup Y=Y$

34.

Consistency Principle

a)

$\left(X\cup Y\right)\cup Z\ =\ X\cup\left(Y\cup Z\right)\$

b)

$X\cup\left(Y\cap Z\right)\ =\ \left(X\cup Y\right)\cap\left(X\cup Z\right)$

c)

$\left(X\cup Y\right)'\ =\ X'\ \cap Y'$

d)

$X\subseteq Y\ \ \ iff\ \ X\cup Y=Y$

35.

Which of the following mathematical concepts is TRUE?

a)

there is no order imposed on the elements of a

set

b)

$<a,b>\ =\ <b,a>$

c)

$\left\{a,b\right\}\ne\left\{b,a\right\}$

d)

in an ordered pair <a,b>, b is the 1st element

36.

Define an ordered pair <a,b> in terms of sets.

a)

{{a}, {a,b}}

b)

{{b},{a,b}}

c)

{{a},{b}}

d)

{a,b}

37.

Define an ordered pair <b,a> in terms of sets.

a)

{{a}, {a,b}}

b)

{{b},{a,b}}

c)

{{a},{b}}

d)

{a,b}

38.

Cartesian Product

a)

$A\times B=\left\{<x,y>\parallel x\in A\ and\ y\in B\right\}$

b)

$A\times B=\left\{x\parallel x\in A\ and\ y\in B\right\}$

c)

$A\times B=\left\{x\parallel y\in A\ and\ x\in B\right\}$

d)

$A\times B=\left\{<y,x>\parallel x\in A\ and\ y\in B\right\}$

39.

What happens if either A or B is $\phi$ ?

Suppose A = {a,b}. What is A × $\phi$ ?

a)

$\phi$

b)

$\left\{\phi,a,b\right\}$

c)

$\left\{\left\{\phi,a\right\},\left\{\left\{\phi,b\right\}\right\}\right\}$

d)

$\left\{\left\{a,\phi\right\},\left\{b,\phi\right\}\right\}$

40.

If K = {a,b,c} and L = {1,2}, then K x L is _______________.

a)

<a,1>

<a,2>

<b,1>

<b,2>

<c,1>

<c,2>

b)

<1,a>

<2,a>

<1,b>

<2,b>

<1,c>

<2,c>

c)

<1,1>

<1,2>

<2,1>

<2,2>

41.

If K = {a,b,c} and L = {1,2}, then L x K is _______________.

a)

<a,1>

<a,2>

<b,1>

<b,2>

<c,1>

<c,2>

b)

<1,a>

<2,a>

<1,b>

<2,b>

<1,c>

<2,c>

c)

<1,1>

<1,2>

<2,1>

<2,2>

42.

If K = {a,b,c} and L = {1,2}, then L x L is _______________.

a)

<a,1>

<a,2>

<b,1>

<b,2>

<c,1>

<c,2>

b)

<1,a>

<2,a>

<1,b>

<2,b>

<1,c>

<2,c>

c)

<1,1>

<1,2>

<2,1>

<2,2>

43.

The Cartesian product is named after (a) .

44.

If A and B are any sets and $R\subseteq A\times B$ ,which of the following is NOT TRUE about R?

a)

a binary relation from A to B

b)

a

binary relation between A and B

c)

a binary relation from B to A

d)

a binary relation between B and A

45.

A relation IN or ON set A.

a)

$R\subseteq A\times A$

b)

$R\subseteq A$

c)

$R\times A$

d)

$A\times R$

46.

$R=\left\{a\parallel<a,b>\in R\ for\ some\ b\right\}$

a)

Domain of the relation R

b)

Range of the relation R

47.

$R=\left\{b\parallel<a,b>\in R\ for\ some\ a\right\}$

a)

Domain of the relation R

b)

Range of the relation R

48.

Complement of a Relation

a)

$R'=\left(A\times B\right)-R$

b)

$R'=R-U$

c)

$R\subseteq A\times B$

d)

$R'=\left(B\times A\right)-R$

49.

What is the complement of the relation $R=\left\{<a,d>,\ <a,e>,\ <b,c>\right\}$ on the universe $\left\{a,b\right\}\times\left\{c,d,e\right\}$ ?

a)

$\left\{<a,c>,\ <b,d>,\ <b,e>\right\}$

b)

$\phi$

c)

Zero

d)

$\left\{<a,b,c,d,e>\right\}$

50.

What is the inverse of a relation $R\subseteq A\times B$ ?

a)

$R'\subseteq B\times A$

b)

$R^{-1}\subseteq A\times B$

c)

$R^{-1}\subseteq B\times A$

d)

$\left(R^{-1}\right)^{-1}$

51.

If $R=\left\{<a,d>,\ <a,e>,\ <b,c>\right\}$ , what is $R^{-1}$ ?

a)

$R^{-1}=\left\{<d,a>,\ <e,a>,\ <c,b>\right\}$

b)

$R^{-1}=\left\{<a,c>,\ <b,d>,\ <b,e>\right\}\$

c)

$R^{-1}=\left\{<c,a>,\ <d,b>,\ <e,b>\right\}$

52.

A relation F from A to B is a function from A to B if and only if

a)

Each element in the domain of F is paired with just one

element in the range

b)

The domain of F is equal to B, domF=B

c)

Each element in the range of F is paired with just one

element in the domain

d)

A function is not a subset R of A × B such that each element of B occurs as the first member of exactly one ordered pair in R

53.

Consider the sets A={a,b} and B={1,2,3}.

Which of the following are NOT FUNCTIONS from A to B?

a)

{<a,1>, <b,1>}

b)

{<a,2>,<b,3>}

c)

{<a,1>}

d)

{<a,2>,<b,1>,<b,3>}

54.

F is a function from A to B

a)

$F:A\rightarrow B$

b)

$F:A\leftrightarrow B$

c)

$F:A-B$

d)

$F:A\times B$

55.

If the range of the function equals B, then the function is onto B.

a)

Surjection

b)

Injection

c)

Bijection

56.

A function $F:A\rightarrow B$ is called one to one function.

a)

Surjection

b)

Injection

c)

Bijection

57.

A function which is both one to one and onto.

a)

Surjection

b)

Injection

c)

Bijection

58.

Which of the following relations are SURJECTIVE?

a)

F only

b)

G only

c)

F and G

d)

G and H

59.

Which of the following relations is INJECTIVE?

a)

F only

b)

G only

c)

F and G

d)

G and H

60.

Which of the following relations is BIJECTIVE?

a)

F only

b)

G only

c)

F and G

d)

G and H

61.

Given two functions $F:\ A\rightarrow B$ and $G:\ B\rightarrow C$ , we may form a new

function from A to C called ___________

a)

$G\ \circ\ F$

b)

$F\ \circ\ G$

62.

If $K=\left\{a,b,c\right\}$ , $L\ =\ \left\{1,2,3,4\right\}$ and $M=\left\{p,q,r\right\}$ ,

then $G\ \circ\ F:\ K\rightarrow M$ is _______________.

a)

$\left\{<a,p>,\ <b,q>,<c,q>\right\}$

b)

$\left\{<a,1>,\ <b,3>,<c,3>\right\}$

c)

$\left\{<1,p>,\ <2,q>,<3,q>,<4,r>\right\}$

63.

Which of the following is NOT TRUE about composition of functions?

a)

G o F is not equal to F o G

b)

G(F(a))

and (G o F)( a) produce the same value

c)

G o F

is equal to

F o G

64.

Given a set A and a relation R in A,

R is REFLEXIVE if and only if

a)

all the ordered pairs of the form <x,x> are in R for every x

in A

b)

for every ordered pair <x,y> in R, the pair <y,x> is also in R

c)

for all ordered pairs <x, y>

and <y,z> in R, the pair <x,z> is also in R

d)

for every two

distinct

elements x and y in A, <x , y>∈R or <y , x>∈R (or both)

65.

Given a set A and a binary relation R in A,

R is SYMMETRIC if and only if

a)

all the ordered pairs of the form <x,x> are in R for every x

in A

b)

for every ordered pair <x,y> in R, the pair <y,x> is also in R

c)

for all ordered pairs <x, y>

and <y,z> in R, the pair <x,z> is also in R

d)

for every two

distinct

elements x and y in A, <x , y>∈R or <y , x>∈R (or both)

66.

A relation R is TRANSITIVE if and only if

a)

all the ordered pairs of the form <x,x> are in R for every x

in A

b)

for every ordered pair <x,y> in R, the pair <y,x> is also in R

c)

for all ordered pairs <x, y>

and <y,z> in R, the pair <x,z> is also in R

d)

for every two

distinct

elements x and y in A, <x , y>∈R or <y , x>∈R (or both)

67.

A relation R in A is connected (or connex)

a)

all the ordered pairs of the form <x,x> are in R for every x

in A

b)

for every ordered pair <x,y> in R, the pair <y,x> is also in R

c)

for all ordered pairs <x, y>

and <y,z> in R, the pair <x,z> is also in R

d)

for every two

distinct

elements x and y in A, <x , y>∈R or <y , x>∈R (or both)

68.

(a) are relations which are reflexive, symmetric

and transitive.

69.

By dividing a set into

mutually exclusive and collectively exhaustive nonempty subsets

we effect what is called (a) .

70.

The subsets that are members off a partition

are called (a) of that partition.

EdMath 301 - Long Quiz - April 15, 2023

Total questions: 70

Worksheet time: 23mins

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