CMPUT272 Lecture Notes - Lecture 18: Binary Relation, Cross Product, Injective Function

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Novemebr 5 2014
ETLC 2-001
Relations
Recall:
A1 ... ai i w = y B) A C)
((a, b), c)
An n-ary relation on the cross product of n sets is a
subset of A1 An
A binary relation on A B
Examples of binary relations:
R +)^2 R = {(x, y) | x R, 1R5, 1 N
{a, b}
R ) R
A binary relation from A to B is a funcion a!bf
(a1, _)
(a2, _)
... (there is no other (a2, _) )
(an, _)
f: A -> B
(a, b) f}
Examples of functions:
f: {1, 2, 3} -> {p, q}
f = {(1,q), (2,q), (3,q)} (ok)
f = {(1,p), (2,p), (3,p)} (ok)
f = -> -> a1,a2 a1 = a2
aka, A, a1 f(a1) a1,a2 a1 = a2
|A| ba |B|
A function f: A -> B is one-to-one
correspondance (aka, bijection, bijective) if
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