Chapter 2: Sets

Question 1

A _____ is an unordered collection of objects, called elements or members of the ____.

Answer 1

Set

Question 2

We write a (E) A to denote that a is _______ of the set.

Answer 2

A is an element of the set.

Question 3

We write a(/E) A to denote that a is _______ of the set.

Answer 3

A is not an element of the set.

Question 4

A = {1, 4, 6, 3, 8} denotes what?

Answer 4

A set of numbers.

Question 5

O = {x | x is an odd positive integer less than 10}.

This is describing a set using ____ _______ notation.

Answer 5

Set Builder.

Question 6

N = { 0, 1, 2, 3, …}, the set of ______ _______.

Answer 6

Natural Numbers

Question 7

Z = {…, -2, -1, 0, 1, 2, …}, the set of ______.

Answer 7

Integers

Question 8

Z^+ = {1, 2, 3, …}, the set of _____ ______.

Answer 8

Positive Integers

Question 9

Q = {p/q | p (E) Z, q (E) Z, and q /= 0}, the set of _____ _____.

Answer 9

Rational Numbers

Question 10

R, the set of ______ ______.

Answer 10

Real Numbers

Question 11

R^+, the set of ______ _____ _______.

Answer 11

Positive Real Numbers

Question 12

C, the set of ______ _____.

Answer 12

Complex Numbers

Question 13

What is interval notation?

Answer 13

[a, b] = {x | a

Question 14

Two sets are ____ if an only if they have the ______ ______.

Answer 14

Equal

Same Elements

Question 15

Are the sets: {1, 3,5 } and {3, 5, 1} equal? Why or why not?

Answer 15

Yes, they have the same elements. (Order does NOT matter)

Question 16

Are the sets: {1, 2, 2, 2, 5, 5, 5, 5} and {1, 3, 5} equal? Why or why not?

Answer 16

Yes, they have the same elements. (Frequency of elements does not matter)

Question 17

0/ or { } denotes an ____ ____ or ____ _____.

Answer 17

Empty Set

Null Set

Question 18

A singleton set is denoted as:

Answer 18

{0/}

Question 19

The single element of the set {0/} is ___________.

Answer 19

The empty set itself.

Question 20

The set A is a ______ of B if and only if every element of A is also an element of B.

Answer 20

Subset

Question 21

The symbol to denote a subset:

Answer 21

C_

Question 22

Theorem 1 states that every nonempty set S is guaranteed to have at least two subsets, the _____ set and the _____ ____ ______.

Answer 22

Empty

Set S Itself

Question 23

When we wish to emphasize that a set A is a subset of a set B but that A /= B, we write ______ and say that A is a _______ ______ of B.

Answer 23

A (C) B

Proper Subset

Question 24

To show that two sets A and B are equal, show that _____ and ______.

Answer 24

A (C_) B

B (C_) A

Question 25

A set A has n distinct elements. N is the _____ of A. This ________ is denoted by _____

Answer 25

Cardinality | | A |

Question 26

The cardinality of |0/| is:

Answer 26

0

Question 27

Given a set S, the ____ ___ of S is the set of all subsets of the set S. The _____ ____ of S is denoted by ______.

Answer 27

Power Set | P(S)

Question 28

What is the power set of {0, 1, 2}? Notation: P( {0, 1, 2} )

Answer 28

{ 0/, {0}, {1}, {2}, {0, 1}, {0, 2}, {1, 2}, {0, 1, 2}}

Question 29

P( 0/ )

Answer 29

{0/}

Question 30

P( {0/} )

Answer 30

{ 0/, {0/}}

Question 31

The ordered pairs (a, b) and (c, d) are equal __________ _____ and ____.

Answer 31

Equal if and only if. | a=c and b=d.

Question 32

The A and B be sets. The ________ _______ of A and B, denoted by A x B, is the set of all ordered pairs (a, b), where a (E) A and b (E) B. Hence, A x B = { (a, b) | a (E) A ^ b (E) B}

Answer 32

Cartesian Product

Question 33

What is the Cartesian Product of A = {1, 2} and B = {a, b, c}? A x B

Answer 33

A x B = { (1, a), (1, b), (1, c), (2, a), (2, b), (2, c) }

Question 34

What is the Cartesian Product of B x A:

Answer 34

B x A = { (a, 1), (a, 2), (b, 1), (b, 2), (c, 1), (c, 2) }

Question 35

What is the Cartesian Product A x B x C, where A = {0, 1}, B = {1, 2}, C = {0, 1, 2}?

Answer 35

A x B x C = { (0, 1, 0), (0, 1, 1), (0, 1, 2), (0, 2, 0), (0, 2, 1), (0, 2, 2), (1, 1, 0), (1, 1, 1), (1, 1, 2), (1, 2, 0), (1, 2, 1), (1, 2, 2) }