Objectives: By the end of class, I will be able to: Identify sets Understand subsets, intersections, unions, empty sets, finite and infinite sets,

Objectives: By the end of class, I will be able to:

Identify sets

Understand subsets, intersections, unions, empty sets, finite and infinite sets, universal sets and complements of a set

SETS

• Set – a well defined collection of elements• A set is often represented by a capital letter.• The set can be described in words or its members or

elements can be listed with braces { } . Example: if A is the set of odd counting numbers less than 10 then we can write:– A = the set of all odd counting numbers less than ten OR– A = {1,3,5,7,9 }– To show that 3 is an element of A, we write: 3 ϵ A– To show 2 is not an element of A, we write : 2 A

SETS

• If the elements of a set form a pattern, we can use 3 dots.

• Example: {1,2,3… } names the set of counting numbers• Another way to describe a set is by using set-builder

notation.• Example: { n | n is a counting number }• This is read – the set of all elements n such that n is a

counting number.

SETS• Finite set – a set whose elements can be counted, and in which the counting

process comes to an end.• Examples:

– The set of students in a class– {2,4,6,8…..200}– {x | x is a whole number less than 20}

• Infinite set – a set whose elements cannot be counted• Examples:

– The set of counting numbers– { 2,4,6,8… }

• Empty set or null set, is the set that has no elements• Examples:

– The set of months that have names beginning with the letter Q– { x | x is an odd number exactly divisible by 2 }

• Symbol for the empty set { } or Ø

• Universal set - is the entire set of elements under consideration in a given situation and is usually denoted by the letter U.

• Example:– Scores on a Math test. U = {0,1,2 …100 }

SETS

• Subsets – set A is a subset of B if every element of set A is an element of set B.

• We write: A B• Example:

– the set A = {Harry, Paul } is a subset of the set B = {Harry, Sue, Paul, Mary }

– The set of odd whole numbers {1,3,5,7… } is a subset of the set of whole numbers, {0,1,2,3… }

SETS

• Union – is the set of all elements that belong to set A or to set B, or to both set A and set B.

• Symbol: A υ B• Example:

– If A = {1,2,3,4 } and B = { 2,4,6 }, then A υ B = {1,2,3,4,6}

• Intersection - is the set of all elements that belong to both sets A and B.

• Symbol: A ∩ B• Example:

– If A = {1,2,3,4,5} and B = {2,4,6,8,10} then A ∩ B = { 2,4 }

SETS

• Complement – is the set of all elements that belong to the universe U but do not belong to the set A.

• Symbol: A or Ac or A` all read A prime• Example:

– If A = {3,4,5} and U = {1,2,3,4,5} , then Ac = { 1,2 }

•Practice with sets

Set notationLet’s review and look at Notes from regentsprep

Set notation

Let’s practice