Simple relation question
Algebra
Level
4
Consider a set A,{1,2,3}. A relation(A to A) is given by {(1,2),(2,3)}. Find the minimum number of ordered pairs to be added to the relation so that the relation becomes an equivalence relation.
The answer is 7.
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1 solution
For a relation to be equivalence relation,it also has to be reflexive,symmetric and transitive.
For reflexive, (1,1),(2,2),(3,3) pair must be added.
For symmetric, (2,1) and (3,2) must be added.
For transitive (1,3) must be added
and Now,pair (3,1) must be added for symmetric. Taking union of all the above,we get 7 pairs.