Let X be the set {1,2,3,4} and let R={(1,1),(1,2),(2,1),(2,2),(3,3),(3,4),(4,3),(4,4) }. Show that R is an equaivalence relation and write down its equvalence classes.
I don't really understand what does equivalence relation mean.
Reflexive:
Transitive:
Symmetric:
For example, this relation is reflexive because 1R1, 2R2, 3R3, 4R4. (As can be seen by noting that .)
You can show that it is symmetric because 1R2 and 2R1, etc. ( ) Note that we need not require that 3R1 because (1, 3) is not in the set R.
I'll leave transitivity to you (that's the long one and I'm lazy. )
-Dan