SETS & SET NOTATION
Set
• It is a collection of objects that have
something in common or follow a rule.
• The objects in the set are called its
elements.
• Set notation uses curly braces, with
elements separated by commas.
A = {coat, hat, scarf, gloves, boots},
• Set A has 5 elements.
• Coat  A
What is the set of all fingers?
What is the set of even numbers between 0 and 10?
Let M = set of the days of the week.
Let X = the set of odd numbers less than 12
B = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
C = {2, 4, 6, 8, 10}
• Subset – is part of a set.
• Set C is a subset of set B.
• We call set B the universal set…Venn Diagram is:
U = {a, b, c, d, e, f, g, h, i, j, k, l, m}
A = {a, c, e, g, i, k, m}
B = {b, d, f, h}
U = {a, b, c, d, e, f, g, h, i, j, k, l, m}
A = {a, c, e, g, i, k, m}
B = {a, b, c, d, e, f}
U = {a, b, c, d, e, f, g, h, i, j, k, l, m}
A = {a, b, d, e, h, j, m}
B = {a, d, e, f, g, h, k}
C = {b, c, f, h, l}
Union
• It is the joining of all elements of two or
more sets
• It is represented as A  B.
A = {letters in the word mathematics}
B = {letters in the word problem}
• Find A  B
A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
B = {set of odd numbers}
C = {multiples of three}
D = {Multiples of four}
Find:
B  C=
CD=
B  D=
BCD=
Intersection
• This consists of the elements that the sets have in
common.
• It is represented as A  B.
A = {letters in the word mathematics}
B = {letters in the word problem}
• Find A  B
A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
B = {set of odd numbers}
C = {multiples of three}
D = {Multiples of four}
Find:
B  C=
CD=
B  D=
BCD=
Shade A  B
Shade A  B
Shade A  B  C
Complement
• Consists of the elements not in that set.
• Represented as A’
• Read “not A”
U = {1, 2, 3, 4, 5, 6, 7,8, 9, 10}
A = { 2, 4, 6, 8, 10}
B = {1, 2, 3, 4, 5, 6, 7}
There are 18 bikes in a parking lot. 7 are gas powered
and 5 are electric powered. 2 bikes are powered by
both gas and electric. How many bikes in the parking
lot are not powered by anything?
A case of chocolate contains 15 chocolate bars. The
chocolates come in three varieties: milk, dark, and milk/dark
mix. 6 milk chocolates and 3 dark chocolates become
expired. How many of the milk chocolates are expired if there
are 6 milk chocolates that are not expired?
• http://www.univie.ac.at/moe/tests/mengen/duv.html
Homework
• Worksheet