Section 2.2 Relations

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Section 2.2 Relations
Try Again

• According to the Unit 4 Framework, a relation
  is rule that gives an output number for every
  valid input number.

A relation is a correspondence between an element
of set A with an element of set B. This means
that for any relation, there is some way to
connect one element of a set to that of another
element in the relation. Lets look at few
examples
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Relations

• A relation R from a set A to a set B is a subset
  of .
• Let R be a relation on a set A.
• R is reflexive if
  .
• R is symmetric means that
  .
• R is transitive means that
• 
  .

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Equivalence Relations

• A relation on a set A is an equivalence relation
  if it is reflexive, symmetric, and transitive.
• Disjoint subsets within an equivalence relation
  are called equivalence classes.

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Example using arrow diagrams

• Look at Example 9 on page 61 of your textbook.
• This figure represents one relation.
• This is an equivalence relation.
• Do you see the reflexive, symmetric, and
  transitive properties?
• This relation has 4 equivalence classes.

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Money Talks!

• Let set Adollar, euro, peso and
• let set BCanada, France, USA.
• Lets define our relation to be
• An element in Set A is a monetary unit in Set
  B.
• The relation consists of the following ordered
  pairs
• (dollar, Canada), (dollar, USA), (euro, France)

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Properties of Relations

• A relation R from a set A to a set B is a subset
  of .
• Let R be a relation on a set A.
• R is reflexive if
  .
• R is symmetric means that
  .
• R is transitive means that
• 
  .

A relation on a set A is an equivalence relation
if it is reflexive, symmetric, and transitive.
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has the same eye color as

• Do you see the reflexive, symmetric, and
  transitive properties? This relation has 3
  equivalence classes.

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is taller than
10
less than or equal to
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Exercise Set 18 (page 65)
Discuss this exercise as a class before looking
at the answers below.
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Graded Assignment for Section 2.2

• Due on Monday
• Exploratory Exercise Set 4
• Exercise Set 16