Chapter 2

Question 1

elements

Answer 1

objects in a set

Question 2

singleton set

Answer 2

contains only one element

Question 3

empty set

Answer 3

also called null set

contains no elements

denoted by 0

Question 4

C

Answer 4

the set of all complex numbers

Question 5

R+

Answer 5

the set of all positive real numbers

Question 6

R

Answer 6

the set of all real numbers

Question 7

Z+

Answer 7

the set of all positive integers (does NOT include 0)

Question 8

Z

Answer 8

the set of all integers

Question 9

set

Answer 9

an unordered collection of distinct objects

Question 10

intersection of a collection

Answer 10

the set that contains those elements that are members of all the sets in the collection

Question 11

union of a collection

Answer 11

the set that contains those elements that are members of at least one set in the collection

Question 12

intersection

Answer 12

A n B

contains those elements in both A and B

Question 13

union

Answer 13

A u B

contains those elements in either A or B

Question 14

P(S)

Answer 14

the power set of S

the set of all subsets of the set S

if n is the number of elements in S, the the power set contains 2^n elements

Question 15

|S|

Answer 15

cardinality of S

length of a finite set

Question 16

a E A

Answer 16

a is an element of A

Question 17

B >= A

Answer 17

B is a superset of A

Question 18

paradoxes

Answer 18

logical inconsistencies

Question 19

A - B

Answer 19

difference

complement of B with respect to A

the set containing those elements that are in A but not in B

Question 20

A X B

Answer 20

Cartesian product

the set of all ordered pairs (a,b), where a E A and b E B

Question 21

roster method

Answer 21

list all members of the set within {}

Question 22

set builder notation

Answer 22

characterize all the elements in a set by stating the property or properties they must have

Question 23

N

Answer 23

the set of all natural numbers (includes 0)

Question 24

intervals

Answer 24

sets of all real numbers between two numbers a and b, with or without a and b

Question 25

A <= B

Answer 25

A is a subset of B

Ax(x E A –> x E B)

Question 26

A < B

Answer 26

A is a proper subset of B

Ax(x E A –x E B) && Ex(x E B && x !E A)

Question 27

A bar

Answer 27

complement of A with respect to the universal set U

U - A

Question 28

multiset

Answer 28

an unordered collection of elements where on element can occur as a member more than once

Question 29

disjoint

Answer 29

two sets are disjoint if their intersection is the empty set

Question 30

truth set

Answer 30

the set of elements x in the domain D for which a predicate P(x) is true

Question 31

relation

Answer 31

a subset of A X B

Question 32

Q

Answer 32

the set of all rational numbers

{p/q | p E Z, q E Z, and q != 0}