Question: Consider the following algorithm which purports to find the smallest equivalence relation which contains a given relation R: First form the reflexive closure of R,

Consider the following algorithm which purports to find the smallest equivalence

Consider the following algorithm which purports to find the smallest equivalence relation which contains a given relation R: First form the reflexive closure of R, to obtain a new relation R' Next, form the transitive closure of R', to obtain a new relation R", Finally, form the symmetric closure of R" to obtain a new relation R". Output R". Use a counterexample to show that this algorithm is incorrect. That is, find a suitable relation R, determine what the output relation R" is, then argue R" is not the correct solution

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