You are here:

Question
Let Q be the graph consisting of vertices and edges of a 3-dimensional cube. Two relations are defined on the vertices of Q.
•   R1={(v,w):the shortest path from v to w has an odd number of edges}.
•   R2={(v,w):the shortest path from v to w has an even number of edges.

a) Exactly one of R1 and R2 is an equivalence relation

b) Both R1 and R2 are equivalence relations

c) None of R1 and R2 is an equivalence relation

Thank you very much.

Equivalence relation
Note:  this is a revised answer

Questioner's Rating
 Rating(1-10) Knowledgeability = 10 Clarity of Response = 10 Politeness = 10 Comment Thank you for the fast response

Volunteer

Expertise

I can answer most questions up through Calculus and some in Number Theory and Abstract Algebra.

Experience

I have had my Bachelor's Degree since 1987 and have been a teacher since 1988. I earned my Masters Degree in Mathematics May 2010. I have been teaching at the same community college since 2002.

Education/Credentials
I have taught 12 years at the community college level, medical college, and technical college as well as a high school instructor and alternative education instructor and charter school instructor.

Awards and Honors
Master's GPA 3.56 Bachelor's GPA 3.34 Post grad work not degree related GPA 4.0