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

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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. R +)^2 r = {(x, y) | x r, 1r5, 1 n. 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| correspondance (aka, bijection, bijective) if. A function f: a -> b is one-to-one f is 1-1 and onto. |a| = |b| if they have the same domain, co-domain, and set of ordered pairs. A function f: a -> b are equal if and only.

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