Question

Let R= {(1,1),(2,2),(3,3),(4,4),(5,5),(1,3),(3,1),(2,4),(4,2),(5,4),(4,5),(2,5),(5,2)}. Is R an equivalence relation on {1,2,3,4,5}? If it is, list the equivalence classes of the relation.

Answer 1

(x,x) are equivalence classes and (x,y),(y,x) are symmetric classes

Answer 2

Is it transitive?

Answer 3

In order to be an equivalence class it needs to be reflexive symmetric and transitive

Answer 4

Its reflexive and syymetric just not sure abt transitive

Answer 5

Reflexive= xRx meaning (x.x) is an element of R which it is

Answer 6

Symmetric = if xRy then yRx So if (x,y) is an element of R then (y,x) is an element of R
Which is the case here

Answer 7

Transitive = if xRy and yRz then xRz meaning if (x,y) and (y,z) is an element of R then (x,z) is an element of R
But There are no elements in R that are in the form (x,y) and (y,z) So there we cant tell if it is transitive. So it my be transitive by default lol