1. ## Relations of sets

This is my question :-

For each of the following relations on the set {2, 3, 4, 5, 6, 7, 8} say whether the relation is reflexive, whether it is symetric, whether it is transitive and whether it is an equivalence relation.

a P b iff a and b have no common factor greater than 1.
a Q b iff the smaller of a and b is greater than 4.
a R b iff a + b is a multiple of 2.

Justify your answers and draw the diagraph for each relation. For those relations that are equivalence relations, describe the equivalence classes.

Right I apologize now for the fact I have not done any working out simply because I don't have a clue how to even start it! I'm trying to learn it now as I go along but don't have much time so thought I would look for help on here as well as the text book (which isn't making sense right now) so I have two points of view on the question. I'm stuck on two more questions which I will post on sperate threads too. Thanks for any help it's much appreciated.

2. Originally Posted by djmccabie
This is my question :-

For each of the following relations on the set {2, 3, 4, 5, 6, 7, 8} say whether the relation is reflexive, whether it is symetric, whether it is transitive and whether it is an equivalence relation.

a P b iff a and b have no common factor greater than 1.
a Q b iff the smaller of a and b is greater than 4.
a R b iff a + b is a multiple of 2.

Justify your answers and draw the diagraph for each relation. For those relations that are equivalence relations, describe the equivalence classes.

Right I apologize now for the fact I have not done any working out simply because I don't have a clue how to even start it! I'm trying to learn it now as I go along but don't have much time so thought I would look for help on here as well as the text book (which isn't making sense right now) so I have two points of view on the question. I'm stuck on two more questions which I will post on sperate threads too. Thanks for any help it's much appreciated.
I'll help with the first one.

So $a\sim b\Longleftrightarrow (a,b)=1$.

This is not reflexive since $2\not\sim 2$ because $(2,2)=2$