Question

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

• A. 64
• B. 36
• C. 12
• D. 6

Answer 1

Answer: (D)

Given that,
$R\to$ 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.
$aRa,\forall a\in A$
That inean minimum number of elements in 'R' should be six
eg, $R=\{(a,a),(b,b),(c,c),(d,d)(e,e),(f,f)\}$