Let S be the set of all points in a plane and R be a relation on S defines as `R={(P,Q):` distance between `P and Q` is less than 2 units} Show that R is reflexive and symmetric but not transitive.

Explanation

`R = {(P,Q):` distance between `P` and `Q` is less than `2` units.

`R` is reflexive as point `P` will have `0` unit distance with `P` which is less than `2`.

So, `(P,P) in R`.

Now,

Let `(P,Q) in R`.

`=>` Distance between `P` and `Q` is less than `2` units.

`=>` Distance between `Q` and `P` is less than `2` units.

`:. (Q,P) in R`.

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