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The wary relation
Definition Let A be a nonempty set.
a) A unary relation on A is simply a subset of A.
b) A binary relation on A is a subset ofthe cartesian product
A XA.
c) A ternary relation on A is a subset ofthe cartesian product
A XA XA.
d) In generał, ifn >1, then an n-ary relation on A is a subset
ofthe cartesian product A XA X... XA, where the
product has
nfactors.
Examples:
1. Let A = {1,2, 3, 4, 5/.
Then R1 ={\, 3} is a unary relation on A.
R2 = /(l, 1, 1), (1, 2, 3), (1, 4, 5), (2, 2, 3)/ is a ternary
relation
on A.
2. Let A be any set. Then R = {{a, a,..., a) : a GA} GAn is
an /?-ary relation on A. It is called the diagonal relation on A.
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