Question

Is the relation R={(1,1),(2,2), (3,3) in A={123}an equivalence relation

Answer 1

Answer:

So in set (A) all ordered pairs are (1, 1), (2, 2) and (3, 3) so all these ordered pairs are in set R so R is a reflexive relation. ... So, R is also a transitive relation. Now as we all know if any relation R satisfying reflexive, symmetric and transitive then it is called as an equivalence relation.

Answer 2

Answer:

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Step-by-step explanation:

Given set A={1,2,3}

Given R={(1,1),(2,2),(3,3)}

Clearly, the relation R is reflexive on A, as (x,x)∈R for all x∈A

Since, there are no ordered pairs of the form (x,y), so no need to check for symmetric and transitive.

Hence, the given relation is smallest equivalence relation on A.