Show that the relation `R` , defined on the set `A` of all polygons as `R={(P_1,\ P_2): P_1` and `P_2` have same number of sides}, is an equivalence relation. What is the set of all elements in `A` related to the right angle triangle `T` with sides 3, 4 and 5?

Explanation

`R={(P_1,\ P_2): P_1` and `P_2` have same number of sides}

`(P_1,\ P_2) in R` as same polygon has same number of sides.

`therefore` R is reflexive.

`(P_1,\ P_2) in R`
`implies P_1` and `P_2` have same number of sides.

`implies P_2` and `P_1` have same number of sides.

`(P_2,\ P_1) in R`

`therefore` R is symmetric.
...