Sets and Set Theory

Question 1

Sets

Answer 1

Unordered collections of objects that can be finite or infinite.

Question 2

Elements

Answer 2

Members of the set

Question 3

Singleton set

Answer 3

Set with exactly one element.

Question 4

The ways to specify sets

Answer 4

1. Description method
2. Roster/Enumeration method
3. Rule method (Set Builder Notation)

Question 5

V = set of all vowels in the English alphabet

Answer 5

Description method.

Question 6

V = {a, e, i, o, u}

Answer 6

Roster/Enumeration method.

Question 7

A = {x|x is a perfect square less than 10}

Answer 7

Rule method.

Question 8

Repeated elements are to be written _.

Answer 8

once

Question 9

Cardinality

Answer 9

Number of elements in a set.

Question 10

Symbol for cardinality

Answer 10

||

Question 11

|S| could be _ or _, depending on the number of elements

Answer 11

finite, infinite

Question 12

|{}|

Answer 12

0

Question 13

|{{}}|

Answer 13

1

Question 14

ℕ

Answer 14

Set of natural numbers = {1, 2, 3, …}

Question 15

W

Answer 15

Set of whole numbers = {0, 1, 2, …}

Question 16

ℤ

Answer 16

{ …, -2, -1, 0, 1, 2, … } = set of integers

Question 17

ℤ+

Answer 17

{ 1, 2, 3, … } = set of positive integers

Question 18

ℤ-

Answer 18

{ …, -3, -2, -1 } = set of negative integers

Question 19

ℚ

Answer 19

{ p/q | p,q E ℤ and q≠0 } = set of rational numbers

Question 20

ℝ

Answer 20

Set of real numbers

Question 21

ℂ

Answer 21

{ a + bi | a,b E ℝ, i = √(-1) } = set of complex numbers

Question 22

A ⊆ B

Answer 22

Every element of A is an element of B

Question 23

B ⊇ A

Answer 23

If and only if A ⊆ B

Question 24

A = B

Answer 24

Every element of A is an element of B and every element of B is an element of A

Question 25

A ⊂ B

Answer 25

Every element of A is an element of B and B has at least one element that is not in A

Question 26

B ⊃ A

Answer 26

If and only if B ⊇ A and there exists an element that is in set B but not in A

Question 27

⊇

Answer 27

Superset

Question 28

⊃

Answer 28

Proper superset

Question 29

⊆

Answer 29

Subset

Question 30

⊂

Answer 30

Proper subset

Question 31

Venn Diagrams

Answer 31

Used to visualise relationships of sets

Question 32

Disjoint sets

Answer 32

Sets that have no common element

Question 33

A U B

Answer 33

The elements are those in A or in B

Question 34

A ∩ B

Answer 34

The elements are those in A and in B

Question 35

A ∩ B are disjoint if…

Answer 35

A ∩ B = {}

Question 36

A - B

Answer 36

Set Difference. The elements are those in A and not in B

Question 37

A’

Answer 37

The elements are in U and not in A

Question 38

Other ways to write A’

Answer 38

-A, or U-Ā

Question 39

{}’

Answer 39

U

Question 40

A U {}

Answer 40

A

Question 41

{} ∩ U

Answer 41

{}

Question 42

A - A

Answer 42

{}

Question 43

Identities for Set Difference: If set A and B are equal then…

Answer 43

A–B = A–A = {}

Question 44

Identities for Set Difference: When an empty set is subtracted from a set…

Answer 44

the result is that set itself (A – {} = A)

Question 45

Identities for Set Difference: When a set is subtracted from an empty set…

Answer 45

the result is an empty set ( {} – A = {} }

Question 46

Identities for Set Difference: When a superset is subtracted from a subset, the result is…

Answer 46

empty set (A – B = {}, if A ⊂ B)

Question 47

Identities for Set Difference: If A and B are disjoint sets then…

Answer 47

A - B = A, and B - A = B

Question 48

Logic and Sets Correspondence: v = _

Answer 48

U

Question 49

Logic and Sets Correspondence: ^ = _

Answer 49

∩

Question 50

Logic and Sets Correspondence: ~ = _

Answer 50

—

Question 51

Logic and Sets Correspondence: T = _

Answer 51

U

Question 52

Logic and Sets Correspondence: F = _

Answer 52

{}

Question 53

Logic and Sets Correspondence: Truth Table = __

Answer 53

Membership Table

Question 54

Logic and Sets Correspondence: T = _ or _

Answer 54

E, 1

Question 55

Logic and Sets Correspondence: F = _ or _

Answer 55

∉, 0

Question 56

(x E A) is the same as…

Answer 56

~ (x E A), or x E A’

Question 57

Irrational numbers

Answer 57

Any real number that cannot be expressed as the quotient of two integers.

Question 58

Composite numbers

Answer 58

A positive integer that has at least one divisor other than 1 and itself. A positive integer that can be formed by multiplying two smaller positive integers.

Question 59

Prime numbers

Answer 59

Numbers that have only 2 factors: 1 and themselves.