Module 4: Sets

Question 1

Set

Answer 1

a well-defined collection of objects

Question 2

A U B or A ____ B

Answer 2

Union ( combination of distinct elements )

Question 3

A ∈ B or A _____ B

Answer 3

belongs to or is an element of

Question 4

A ∉ B or A ____ B

Answer 4

does not belong to or is not an element of

Question 5

Two types of Set Descriptions

Answer 5

Enumeration or Roster Method and Rule method

Question 6

Enumeration or Roster Method

Answer 6

Elements in a set are listed down

Question 7

Rule Method

Answer 7

Elements in a set are described

Question 8

True of False: The order of the elements in a set matters.

Answer 8

FALSE

Question 9

Equal Sets (A=B)

Answer 9

Two sets A and B are equal if both sets have EXACLTY THE SAME elements

Question 10

Finite Set

Answer 10

It is possible to list down all of its elements

Question 11

Infinite Set

Answer 11

All of its elements cannot be listed down

Question 12

Cardinality of a Set

Answer 12

The number of elements contained in the set

Question 13

Empty or Null Set (set wit no elements) is denoted by ____ or ____.

Answer 13

Ø or {}

Question 14

Universal Set or U

Answer 14

the set consisting of all elements in a particular discussion

Question 15

A ∩ B or A ____ B

Answer 15

Intersection (distinct elements found in BOTH A and B)

Question 16

A \ B or A ____ B

Answer 16

Difference ( Distinct elements in A but not in B )

Question 17

Ac or ______ of A

Answer 17

Complement (Distinct elements NOT in A)

Question 18

A x B or _________ of A and B

Answer 18

Cartesian Product [ order of elements is important because the product is an ordered pair: (a,b) is not the same as (b,a) ]

Question 19

The union and intersection of sets A and B belonging to a universal set U satisfy which two properties

Answer 19

Commutative and Associative Properties

Question 20

TRUE OR FALSE: The set difference does not satisfy the commutative and associative properties.

Answer 20

TRUE

Question 21

1st Formula for Cardinality: number of elements in A intersection B

Answer 21

n(A ∩ B) = n(A) + n(B) − n(A ∩ B)

Question 22

2nd Formula for Cardinality: number of elements in complement of A

Answer 22

n(Ac) = n(U) − n(A)

Question 23

3rd Formula for Cardinality: number of elements in A difference B

Answer 23

n(A \ B) = n(A) − n(A ∩ B)

Question 24

4th Formula for Cardinality: number of elements in the cartesian product of A and B

Answer 24

n(A x B) = n(A) · n(B)

Question 25

A ≠ B or A ____ B

Answer 25

not equal to

Question 26

A ⊆ B or A _____ B

Answer 26

Subset (every distinct element of A is in B)

Question 27

A ⊈ B or A _____ B

Answer 27

is not a subset of

Question 28

A ⊂ B or A _____ B

Answer 28

Proper Subset (every element of A is in B, but B has more elements)

Question 29

A∼B or A ____ B

Answer 29

is equivalent to (A and B have the SAME NUMBER of elements)

Question 30

1st Property satisfied by A=B, given that A∼B

Answer 30

Reflexivity (if A=B, then B=A; therefore, if A∼B, then B∼A)

Question 31

2nd Property satisfied by A=B, given that A∼B

Answer 31

Symmetry (if A=B then B=A; therefore, if A∼B, then B∼A)

Question 32

3rd Property satisfied by A=B, given that A∼B

Answer 32

Transivity (if A=B and B=C, then A=C; therefore, if A∼B and B∼C, then A∼C)

Question 33

One-to-One Correspondence

Answer 33

If and only if every element of A corresponds to exactly one element of B and every element of B corresponds to exactly one element of A (if there exists a bijection from set A onto B)

Question 34

Aleph-null

Answer 34

the lowest level of infinity

Question 35

TRUE OR FALSE: A set with a cardinality of aleph-null or the lowest level of infinity is infinite.

Answer 35

FALSE