
Relations
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, antisymmetric, or transitive? Can the friendship relation among a finite group of people induce a partial order, such as a set inclusion?

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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.

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But do you know what a symmetric relation is? What a relation is in general?

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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.

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OK, so you know what a binary relation is. Do you know which relations are called reflexive, symmetric, etc.?

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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!