Section 9 Chapter 51 - Sets

Question 1

Set

Answer 1

An unordered collection of values where each value appears at most once

Question 2

Methods to define a set (3)

Answer 2

• Listing each number
• Set comprehension
• Compact representation

Question 3

Symbol for empty set

Answer 3

∅

Question 4

Symbol for rational number set

Answer 4

Q

Question 5

Definition for the set of real numbers

Answer 5

The set of all possible real world quantities

Question 6

Finite set

Answer 6

A set where each element can be counted off by natural numbers up to a particular number

Question 7

Cardinality of a finite set

Answer 7

The number of elements in the set

Question 8

Infinite set

Answer 8

A set where you cannot count off each element by natural numbers up to a particular number. It is a set which is not a finite set

Question 9

Countably infinite set

Answer 9

A set that can be counted off by the natural numbers

Question 10

Countable set

Answer 10

A set which can be counted off against a subset of the natural numbers

Question 11

Set comprehension

Answer 11

A method of defining a set where you specify specify some function of n and for which values that function should be run for

Question 12

Symbol for “such that”

Answer 12

|

Question 13

Symbol for membership

Answer 13

∈

Question 14

Symbol for and

Answer 14

∧

Question 15

Write the set {1,4,9,16,25} using set comprehension

Answer 15

A = {n^2 | n < 6 ∧ n ∈ N}

Question 16

Compact representation

Answer 16

A method of defining a set using string-like properties

Question 17

Write the set {01, 0011, 000111…} using compact representation

Answer 17

A = {0^n 1^n | n > 0 ∧ n ∈ N}

Question 18

Empty set

Answer 18

The set with no elements

Question 19

Cartesian product of two sets

Answer 19

The set of all ordered pairs (a,b) where a is a member of A and b is a member of B

Question 20

{1,2,3}x{3,2}

Answer 20

{(1,3), (1,2), (2,3), (2, 2), (3,3), (3,2)}

Question 21

Subset

Answer 21

A is a subset of B if every element in A is also in B

Question 22

Proper subset

Answer 22

A is a proper subset of B if every element in A is also in B and A does not equal B

Question 23

Symbol to show A is a subset of B

Answer 23

A⊆B

Question 24

Symbol to show A is a proper subset of B

Answer 24

A⊂B

Question 25

Union of A and B

Answer 25

A set of every element that is in A or B (or both)

Question 26

Intersection of A and B

Answer 26

A set of every element that is in both A and B

Question 27

Symbol for union

Answer 27

∪

Question 28

Symbol for intersection

Answer 28

∩

Question 29

Difference of sets A and B

Answer 29

Every element that is a member of A but not a member of B