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.

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- August 6th 2007, 10:55 PMr7irisequalvalence relation
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. - August 6th 2007, 11:17 PMtukeywilliams
An equivalence relation is reflexive, transitive, and symmetric.

- August 6th 2007, 11:29 PMr7iris
that's what I don't understand about.

- August 7th 2007, 08:36 AMtopsquark
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