Question

Given the relation `R={(1,2),(2,3)` on the set `A={1,2,3},` add a minimum number of ordered pairs so that the enlarged relation is symmetric, transitive and reflexive.

Answer 1

Correct Answer - 7
`R` is reflexive if it contains `(1,1),(2,2),(3,3)`
`:.(1,2)epsilonR,(2,3)epsilonR`.
Now `R={(1,2),(2,2),(3,3),(2,1),(3,2),(2,3),(1,2)}`
`R` will be transitive if `(3,1),(1,3)epsilonR`. Thus `R` becomes an equivalence relation by adding `(1,1),(2,2),(3,3),(2,1),(3,2),(1,3),(3,1)`
Hence the total no. of ordered pairs `7`.