Set Theory

Question 1

What is a set?

Answer 1

A set is an unordered collection of different types of objects.

Question 2

What is a set’s roster notation?

Answer 2

The roster notation definition of a set is a list of the elements enclosed in curly braces with the individual elements separated by commas.

Question 3

What is an empty set, also known as a null set?

Answer 3

The set with no elements is called the empty set and is denoted by the symbol ∅. Null set denoted “{}”.

Question 4

What is a finite set?

Answer 4

A finite set has a finite number of elements.

Question 5

What is an infinite set?

Answer 5

An infinite set has an infinite number of elements.

Question 6

What is a set’s cardinality, and how is it denoted?

Answer 6

The cardinality of a finite set A, denoted by |A|, is the number of elements in A.

Question 7

What is the universal set?

Answer 7

The universal set, usually denoted by the variable U, is a set that contains all elements mentioned in a particular context.

Question 8

What makes set A a subset of B?

Answer 8

If every element in A is also an element of B, then A is a subset of B, denoted as A ⊆ B.

Question 9

What is a subset?

Answer 9

If A ⊆ B and there is an element of B that is not an element of A (i.e., A ≠ B), then A is a proper subset of B, denoted as A ⊂ B.

Question 10

What is a power set of a set?

Answer 10

The power set of a set A, denoted P(A), is the set of all subsets of A.

Question 11

What is the intersection of two set?

Answer 11

The intersection of A and B, denoted A ∩ B and read “A intersect B”, is the set of all elements that are elements of both A and B.

Question 12

What is the union of two sets?

Answer 12

The union of two sets, A and B, denoted A ∪ B and read “A union B”, is the set of all elements that are elements of A or B.

Question 13

What is the difference of two set?

Answer 13

The difference between two sets A and B, denoted A - B, is the set of elements that are in A but not in B.

Question 14

What is the symmetric difference of two sets?

Answer 14

The symmetric difference between two sets, A and B, denoted A ⊕ B, is the set of elements that are a member of exactly one of A and B, but not both.

Question 15

What is the complement of two sets?

Answer 15

The complement of a set A, denoted A, is the set of all elements in U that are not elements of A.

Question 16

What is a set identity?

Answer 16

A set identity is an equation involving sets that is true regardless of the contents of the sets in the expression.

Question 17

What is an ordered pair?

Answer 17

An ordered pair of items is written (x, y).

Question 18

What is an entry in an ordered pair?

Answer 18

The first entry of the ordered pair (x, y) is x and the second entry is y.

Question 19

What is a Cartesian product of two sets?

Answer 19

For two sets, A and B, the Cartesian product of A and B, denoted A x B, is the set of all ordered pairs in which the first entry is in A and the second entry is in B.
ordered triple

Question 20

What makes two sets disjoint?

Answer 20

Two sets, A and B, are said to be disjoint if their intersection is empty (A ∩ B = ∅)..

Question 21

What makes two sets pairwise disjoint?

Answer 21

A sequence of sets, A1, A2, …, An, is pairwise disjoint if every pair of distinct sets in the sequence is disjoint (i.e., Ai ∩ Aj = ∅ for any i and j in the range from 1 through n where i ≠ j)..