Let `A={1,\ 2,\ 3}` . Then, show that the number of relations containing (1, 2) and (2, 3) which are reflexive and transitive but not symmetric is three.

Explanation

The smallest reflexive relation on set A containing `(1, 2) and (2, 3)` is


`R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3)}`


Since `(1, 2)` belongs to R and` (2, 3)` belongs to R but `(1, 3)`
does not belong to R. So, R is not transitive.
To make it transitive , include `(1, 3) `in R.


`R1 = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)}`


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