MAT 1320 Study Guide - Final Guide: Logical Equivalence, Equivalence Class, Disjoint Sets

• School: University of Ottawa
• Department: Mathematics
• Course: MAT 1320
• Professor: Kirill Zaynullin

Document Summary

Elizabeth maltais: equivalence relations, classes, & partitions, an equivalence relation on a set a is a relation that is re exive, symmetric, and transitive. Equality: = is an equivalence relation on . for all. X=x is reflexive : for all x. , y elr, ( x = y : for all x , y , zeb , (( x - Y ) a ( y =d ] Let a be the set of all compound propositions. Logical equivalence is a relation on a given by the rule: for all p, q 2 a, p q if and only if p $ q is a tautology. Prove that is an equivalence relation on a. Given an equivalence relation r on a, for each element a 2 a, we de ne the equivalence class of a with respect to r as follows: { x ea : a rx } set of all elements of a which are related to a by r.