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