Q.
Let A={1,2,3} and R={(1,2),(2,3)} be a relation in A. Then, the minimum number of ordered pairs may be added, so that R becomes an equivalence relation, is
2824
207
Relations and Functions - Part 2
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Solution:
The given relation is R={(1,2),(2,3)}
in the set A={1,2,3}
Now, R is reflexive, if(1,1),(2,2),(3,3)∈R R is symmetric, if(2,1),(3,2)∈R
R is transitive, if (1,3) and (3,1)∈R.
Thus, the minimum number of ordered pairs which are to be added,
so that R becomes an equivalence relation, is 7 .