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Chapter 6 Relations
Phineas:
Ferb:
Phineas:
And therefore, through the transitive property of belief, you do believe in yourself !
―Phineas and Ferb Season 2 (2010)
Relationships between sets occur in many different contexts. For example, we deal with relationships between people all the time. e.g., Alice is dating Bob. Bob is friends with Eve. Eve and Alice are sisters. We also deal with relationships between other sets. e.g., Four quarters are worth $1. Ten dimes are worth $1.
Relationships between elements of sets are described mathematically using a structure called a
relation , which is just a subset of the Cartesian product of the sets. For example, in the friendship example above, friendship is the relation
\(F\) and
\((\text{Bob}, \text{Eve})\) is an element in
\(F\text{.}\)
