I came across an interesting question and am curious on how to answer it.
What sort of relation is friendship? Is it necessarily reflexive, symmetric, anti-symmetric, or transitive? Can the friendship relation among a finite group of people induce a partial order, such as a set inclusion?
April 2nd 2013, 11:36 AM
What do you think?
I read a joke recently. A man with a multiple personality disorder who found himself on an uninhabited island soon found a lot of friends.
April 2nd 2013, 11:43 AM
I really don't know...
April 2nd 2013, 11:45 AM
But do you know what a symmetric relation is? What a relation is in general?
April 2nd 2013, 11:54 AM
This chapter discusses relation as a mathematical term. For sets A, B, any subset of A x B is called a (binary) relation from A to B. Any subset of A x A is called a (binary) relation on A.
I have no idea how to apply this to the question.
April 2nd 2013, 12:39 PM
OK, so you know what a binary relation is. Do you know which relations are called reflexive, symmetric, etc.?
April 2nd 2013, 12:59 PM
In other words, do you know the definitions of any of those words? When you are doing a math problem and see words whose definitions you do not know, look them up in your textbook!