MATH 113 Chapter Notes -Binary Relation, Equivalence Class, Isomorphism
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Algebra make sure that it"s associative. (a+b)+c = a+(b+c) Two sets are equal if they have the same elements, regardless of order and repetition. P(s) is a set the set of all subsets of s. Partition definition: a collection of nonempty subsets of s such that every element of s is in exactly one subset. Cartesian product definition: s x r so that {(x, y) | x s, y r} Binary relation definition: a binary relation on s is a subset of s x s, sometimes s2. Equivalence relation definition: a binary relation r on s is an equivalent relation iff: Function definition: subset of x x y such that for all x in x, there is a y in y such that (x, y) is in f. Binary operation definition: a function from s x s to s. written as (s, *) where s is a set and.
