SET THEORY

Question 1

A set

Answer 1

is a collection of distinct ‘objects’. We usually use upper case letters to denote sets. For example, we show the set of integers between 1 and 10 as follows:

A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Question 2

An element

Answer 2

An object in a set is also called an element of the set. We use the symbol ∈ to denote the membership of elements and ∉ to denote that an element is not in a set. For example, 3 ∈ A, but 12 ∉ A. We can use ∈ to define new sets.

Question 3

The Universal Set

Answer 3

The universal set is the set of all elements in a domain. We usually use U to denote a universal set. For example:

Todo incluido

Question 4

Venn Diagram

Answer 4

A Venn Diagram shows the logical relationship of sets using geometric shapes such as ovals and circles. Using the same dice example from above,

Question 5

Subsets

Answer 5

Set B is a subset of set A if all elements of set B are also in set A. This is denoted as B ⊂ A. Set A, in this case, is known as the

superset. For example, for the given sets below:

A = {1, 3, 5}

B = {1, 5}

Question 6

Set Operators

Answer 6

The complement of set A is all of the elements in the universal set U but not in A. We denote a compliment as Ac. Using the example of rolling dice:

U = {1, 2, 3, 4, 5, 6}

A = {1, 3, 5}

Ac = {2, 4, 6}

Question 7

Set Difference

Answer 7

Given sets A and B, the difference between A and B is the set of all elements in A that are not in B. This is denoted as A – B. For example, given the following sets:

A = {1, 3, 5}

B = {4, 5, 6}

A – B = {1, 3}

Question 8

Intersections

Answer 8

An intersection of sets A and B is the set that contains all elements that are both in A and B. Intersection is denoted as A ∩ B. Figure 6 shows an example of an intersection of sets A and B.

Question 9

Unions

Answer 9

The union of sets A and B is the set that contains all of the elements from set A and set B. This set is denoted as A ∪ B. It will include elements only from set A, elements only from set B, and elements from the intersection of sets A and B.