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Let S be the set of all points in a plan...

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.

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(i) Reflexive-
`d(A, A) < 2` we get `(A, A) ∈ R `
(ii) Symmetric-
` (A, B) ∈ R `
We get `d (A, B) < 2` and `d (B, A) < 2`
...
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