Transcript Set notation

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:
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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
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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}
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Infinite set – a set whose elements cannot be counted
Examples:
– The set of counting numbers
– { 2,4,6,8… }
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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 notation
Let’s review and look at Notes from regentsprep
Set notation
Let’s practice