A set is an unordered collection of objects without repetition. The set notation

is read as, "the set whose members are red, white, and blue".

Is the following a set?

This is not a set because there are duplicates. That is, red appears twice.

Consider the following sets.

Are these the same sets? These are the same sets because the ordering of the set members does not matter.

Why are bags important?

Many word analysis algorithms for text comparison work on a bag of words model.

A bag, or multiset, is a set where objects can appear more than once.

Python supports sets and set operations.

Here is the Python code [#1]
set1 = { "red", "white", "blue" } for element1 in set1: print("{0:s}".format(element1))
Here is the output of the Python code.
white blue red

The empty set is written as follows.

However, in Python empty curly braces represents an empty dictionary.

In Python, use set() to get an empty set.

Python supports the following set operations.

• add()
• update()
• discard()
• remove()
• pop()
• clean()

A set can be named.

Set A is the set whose members are red, white, and blue.

Note: In mathematics, an upper case letter is often used to name a set. In computers, an upper case letter/name is usually a constant.

The notation is read as "white is a member of the set A".

The universe is the set of all possible elements under consideration.

A Venn diagram, named after John Venn (inventor of Venn diagrams) , is a pictoral representation of sets and set relationships.

The simplest Venn diagram represents the universe U as a rectangle. What is the universe for the roll of a six-sided die? The universe for the roll of a 6-sided die is (the set) as follows.

This Universe is the sample space of a 6-sided die - all the possible values.

What is the difference in meaning of the following two sentences?

• The members of the basketball team compliment each other very well.
• The members of the basketball team complement each other very well.

Note: Both compliment and complement come from the Latin word "complere" meaning to complete The term complement means a nice thing said about something or someone. One meaning of the term compliment is "nice words" as in an "act of praise".

• The members of the basketball team complement each other very well.

Thank you very much. The term complement means one or more things that together form a unit. One meaning of the term complement is "one of two things" that, together, form a unit.

• The members of the basketball team compliment each other very well.

Some complementary colors are as follows.

• red and green (Christmas)
• purple and yellow (Easter)
• orange and blue (Savannah State University)

The complement of set A consists of all those members of the universe who are not in set A. The logical operation NOT, math symbol "¬", is related to the complement set operation. What is { 2, 4, 6 }^c for the roll of a six-sided die?

{ 2, 4, 6 }^c = { 1, 3, 5 }

An intersection of two things is the part that both items have in common. Two lines in a plane either intersect at a point or are parallel.

A traffic intersection is the part that is in common between two roads.

The intersection of sets A and B consists of all those members who are in both set A and set B. The logical operation AND, math symbol "∧", is related to the intersection set operation. What is { 2, 4, 6 } ∩ { 1, 2, 3 } for the roll of a six-sided die?

{ 2, 4, 6 } ∩ { 1, 2, 3 } = { 2 }

Here is the Python code [#2]
a1 = { 2 , 4 , 6 } b1 = { 1 , 2 , 3 } c1 = a1.intersection(b1) # or use the operator as: c1 = a1 & c1 a2 = str(a1) b2 = str(b1) c2 = str(c1) print("A={0:s}".format(a2)) print("B={0:s}".format(b2)) print("C={0:s}".format(c2))
Here is the output of the Python code.
A={2, 4, 6} B={1, 2, 3} C={2}

A union includes everything from the joining together of both parts. The Soviet Union consisted of a union of a number of states (e.g., Russia, Ukraine, etc.).

Each year, the President gives a "State of the Union" speech.

• Before the Civil War: The United States are a country.
• After the Civil War: The United States is a country.

The union of sets A and B consists of all those members who are in either A or set B or both. The logical operation OR, math symbol "∨", is related to the union set operation. What is { 2, 4, 6 } ∪ { 1, 2, 3 } for the roll of a six-sided die?

{ 2, 4, 6 } ∪ { 1, 2, 3 } = { 1, 2, 3, 4, 6 }

Here is the Python code [#3]
a1 = { 2 , 4 , 6 } b1 = { 1 , 2 , 3 } c1 = a1.union(b1) # or use the union operator as: c1 = a1 | b1 a2 = str(a1) b2 = str(b1) c2 = str(c1) print("A={0:s}".format(a2)) print("B={0:s}".format(b2)) print("C={0:s}".format(c2))
Here is the output of the Python code.
A={2, 4, 6} B={1, 2, 3} C={1, 2, 3, 4, 6}

Sets A and B are said to be mutually exclusive if they have no members in common.

{ 2, 4, 6 } ∩ { 1, 3, 5 } = { }

Sets A and B are said to be collectively exhaustive if they include all members in the universe.

{ 2, 4, 6 } ∪ { 1, 3, 5 } = U

It is possible for A and B to be both mutually exclusive and collectively exhaustive.

{ 2, 4, 6 } ∩ { 1, 3, 5 } = { }

{ 2, 4, 6 } ∪ { 1, 3, 5 } = U

The Python set difference operator is "-" (minus sign, example omitted).

The Python symmetric set difference operator is "^N" (caret, example omitted).

The Python membership operator is "in" (example omitted).