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  4. Let R be an equivalence relation defined on a set containing 6 elements. The minimum number of ordered pairs that R should contain is

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Q. Let $ R $ be an equivalence relation defined on a set containing $6$ elements. The minimum number of ordered pairs that $R$ should contain is

KCETKCET 2010Relations and Functions - Part 2

Solution:

Given that,
$R \rightarrow$ equivalence relation on a set $A$
Let $A=\{a, b, c, d, e, f\}$
Since, $R$ is an equivalence relation on set $A$, then it must be satisfies reflexive property, for this.
$a R a, \forall a \in A$
That inean minimum number of elements in 'R' should be six
eg, $R=\{(a, a),(b, b),(c, c),(d, d) (e, e),(f, f)\}$