Give three examples showing that a relation can satisfy any one of reflexivity,

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think I have a really good way of explaining this so I would like comments. My example of an equivalence relation is x and y have the same parity in other words xRy is true when both x and y are odd. xRy is also true when both x and y are even. If one of the variables x,y is odd or even then xRy false. So xRy is true when x and y are the "same"(equivalent) in some respect. if xRy is true x and y have a specific common property. Exactly what the common property is depends on the problem. This explains all your rules. symmetric xRy => yRx If x has a common property with y then y must have a common property with x. reflexive xRx x and x must have a common propery! transitive xRy and xRz => yRz. If x and y have a common property and x and z have a common property then y and z share a common property. Now cleary an equivalence relation divides the set into distint subset where everything each subset has the same common property. if you remember my original example where the equivalence relation is " both odd or both even" then two subsets are the even numbers and the odd numbers and xRy => x and y are in the same subset.

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