SCC121: (W1-L2) Sets - Part 2

Question 1

What is set A if A = {a, b, c}?


Answer 1

A is a set containing elements a, b, and c

Question 2

What does the notation a ∈ A signify?


Answer 2

Element a belongs to set A

Question 3

What does the notation m ∉ A signify?


Answer 3

Element m does not belong to set A

Question 4

How would you express the set of natural numbers x such that x < 10?


Answer 4

{x | x ∈ N and x < 10}

Question 5

What does the union of two sets A and B represent?


Answer 5

Elements in A, or B, or both

Question 6

What is the Cartesian product of two sets A and B?


Answer 6

The set of all possible ordered pairs from A and B

Question 6

What does the intersection of two sets A and B represent?


Answer 6

Elements common to both A and B

Question 7

What is the definition of an empty set?


Answer 7

The empty set is the set which contains no objects

Question 8

What are the notations for the empty set?


Answer 8

{ } or the symbol ∅

Question 9

How can you identify disjoint sets?


Answer 9

Two sets are disjoint if their intersection is the empty set

Question 10

Give an example of two disjoint sets.


Answer 10

{New York, Washington} and {3, 4}

Question 11

What does it mean if two sets are equal?


Answer 11

They have the same elements

Question 12

How is equality of sets denoted?


Answer 12

A = B

Question 13

What does it mean if two sets are not equal?


Answer 13

They do not have identical elements

Question 14

Provide an example of not equal sets.


Answer 14

A = {a, b, c, d, e} and B = {d, b, c, e}

Question 15

What is the cardinality of a set?


Answer 15

The number of elements in the set

Question 16

What is a set of sets?


Answer 16

A set that contains other sets as elements

Question 17

If A = {1, 2, 3, 4, 5}, what is |A|?


Answer 17

|A| = 5

Question 18

What is the cardinality of the empty set?


Answer 18

|∅| = 0

Question 19

If B = {∅, {a}, {b}, {a, b}}, what is |B|?


Answer 19

|B| = 4

Question 20

What is a subset?


Answer 20

Set A is a subset of set B if every element of A is also in B
Denoted as A ⊆ B

Question 21

How can you determine if A is a subset of B?


Answer 21

If every element in A is also in B

Question 22

If A = {a, b, c} and B = {a, b, c, d, e}, is A a subset of B?


Answer 22

Yes, A ⊆ B

Question 23

What does it mean if A is not a subset of B?


Answer 23

There is at least one element in A which is not in B

Question 24

If A = {1, 2, 3} and B = {4, 5}, is A a subset of B?


Answer 24

No, A ⊈ B

Question 25

Is every set a subset of itself?


Answer 25

Yes, A ⊆ A

Question 26

What is a proper subset?


Answer 26

A is a proper subset of B if every element in A is also in B and there is at least one element in B that is not in A

Question 26

If A = {a, b, c} and B = {a, b, c, d, e}, how would you denote that A is a proper subset of B?

Answer 26

A ⊂ B

Question 27

What is a superset?


Answer 27

B is a superset of A if every element of A is also an element of B

Question 28

If B = {a, b, c, d, e} and A = {a, b}, how would you denote that B is a superset of A?


Answer 28

B ⊇ A

Question 29

What is a proper superset?


Answer 29

B is a proper superset of A if there is at least one element in B which is not in A

Question 30

What is a universal set?


Answer 30

A universal set is a non-empty set of all possible elements relevant to a specific problem

Question 31

How is the universal set usually denoted?


Answer 31

By the symbol U

Question 32

What is the complement set?


Answer 32

The complement set is the difference between the universe and a given set

Question 33

If U = {red, orange, yellow, green, blue, indigo, violet} and A = {red, yellow, blue}, what is comp(A)?


Answer 33

comp(A) = {orange, green, indigo, violet}

Question 34

What symbol is this?
∅

Answer 34

empty set - set with no elements

Question 35

disjoint sets

Answer 35

sets whose intersection is the empty set

Question 36

A = B

Answer 36

• equal sets - sets with the same elements

Question 37

A ≠ B

Answer 37

not equal sets - sets which do not have the same elements

Question 38

|A|

Answer 38

set cardinality - number of elements in a set A

Question 39

A ⊆ B

Answer 39

• subset - elements of set A are also in set B

Question 40

A ⊂ B

Answer 40

proper subset - A is subset and there is at least one element in set B that is not in set A

Question 40

B ⊇ A

Answer 40

• superset - elements of set A are also in set B

Question 41

B ⊃ A

Answer 41

• proper superset - B is superset and there is at least one element in set B that is not in set A

Question 42

U

Answer 42

• universal set - set of all possible elements relevant to a specific problem