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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 issymmetric, transitive and reflexive. |
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Answer» 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`. |
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