MATH-0061 Study Guide - Midterm Guide: Symmetric Relation, Partially Ordered Set, Surjective Function

• School: Tufts University
• Department: Mathematics
• Course: MATH-0061
• Professor: all

Document Summary

[20 mins] consider a set s = {x, y, z}. As you know, a relation is any r s s. (for instance, equality is the relation r0 = {(x, x), (y, y), (z, z)}, which has three elements. ) That means that the set of all relations on s is r = p(s s). Yes, is the minimum because r r r. On the other hand, s s is the maximum because r s s. Since |s| = 3, the cartesian product has order |s s| = 9, which means that |r| = |p(s s)| = 29 = 512. (c) give an example of a symmetric relation on s with ve elements. A function f : s s is a relation f s s such that s s, !s s such that (s, s ) f . In other words, every input from s has exactly one associated output from s.