MATH 113 Lecture Notes - Lecture 2: Binary Relation, Empty Set, Binary Operation
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Empty set, with a slash, sometimes {} the unique set with no elements. Two sets are equal if they have the same elements, regardless of order and repetition. P(s) the set of all subsets of s. P{a, b} = { , {a}, {b}, {a, b}} Not the same as just the empty set! S x r the cartesian product of sets s and r. { (x, y) : x s, y r } But it doesn"t regularly, like in {x, y} A binary relation on s is a subset of s x s. sometimes written. Def: a binary relation r on s (r c s x s) is an equivalence relation if: (written as xry, not. For every x, y s, (x, y) r => (y, x) r. For every x, y, z s, (x, y) r & (y, z) r => (x, z) r.
