(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I have got myself very confused about equivalence relations. I have to determine whether certain relations R are equivalence relations (and if they are describe the partition into equivalence classes, but I'll worry about that once I understand the first part).

Here are some of the relations:

i) S = {x is a real number| x>0}; aRb iff ab = 1

ii) S = R^3\ {0}; vRw iff there is a 1 dimensional subspace of the vector space R^3 which contains v and w.

I have several other relations to consider but is someone could give me some ideas with these, hopefully I will be able to transfer my understanding to the others.

Many thanks.

2. Relevant equations

3. The attempt at a solution

i) S = {x is a real number| x>0}; aRb iff ab = 1

If my understanding is correct, this is not an equivalence relation as aRa is not true for all a in S, e.g. if a = 2 then 2*2=4 is not equal to 1, so R is not reflexive.

ii) S = R^3\ {0}; vRw iff there is a 1 dimensional subspace of the vector space R^3 which contains v and w.

I have no idea on this one.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Equivalence relations

**Physics Forums | Science Articles, Homework Help, Discussion**