Define Relation.
a binary relation R on a set S is a set of pairs of elements of S. In other words, R⊆ S x S. In other words, R is a set of edges in a directed graph with vertices S.
Relations can relate more than two sets. In general, a relation on S, T, U,..... is a subset of S x T x U x ......
Example: a database table can be thought of as a set of rows; each row can be thought of as a tuple. Thus the table is a relation on S, T, U,..... where S is the set of possible values for the first column, T is the set of possible values for the second column, and so on.
Notation: if R is a binary relation and (x,y) ∈ R we write xRy. this generalizes relations like “ = ” and “ ≤ ”.
relations generalize functions. You can think of a function F as a relation: yFx if y= F(x). relation composition (as defined last lecture) is than the same as function composition.
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