Equivalence relations and their properties

Equivalence relations in geometry

Equivalence in biology - meaning, definition and examples

SOLVED:a) What is the equivalence class of (1,2) with respect to the equivalence relation in Exercise 16? b) Give an interpretation of the equivalence classes for the equivalence relation R in Exercise 16 . I Hint: Look at the ratio a / b corresponding to (a, b) . ]

7.5.5 Consider the relation   defined on Z × IN = (x,y) : x ? Z, and y ? N by(a,b) (c,d) ? ad = bc.(a) Prove that   is an equivalence relation.(b) List several elements of the equivalence class of (2,3). Repeat for the equivalence class of(-3,7). What do the equivalence classes have to do with the set of rational numbers Q?(c) Define operations ⊕ and ⊗ on Z × IN/  by[(a,b)] ⊕ [(c,d)] = [(ad bc, bd)],[(a,b)] ⊗ [(c,d)] = [(ac, bd)].Prove that ⊕ and ⊗ are well-defined.Try to do this question with

For each equivalence relation below, find the requested equival... | Filo