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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
Let $A = {0,1,2,\ldots,9}$. Let $R$ be a relation on $A$ defined by $(x,y) \in R$ iff $|x-y|$ is a multiple of $3$.
Given below are two statements:
Statement I: $n(R) = 36$
Statement II: $R$ is an equivalence relation
Choose the correct option:
Solution
Classes:
$0,3,6,9 \Rightarrow 4$
$1,4,7 \Rightarrow 3$
$2,5,8 \Rightarrow 3$
Total relations
$= 4^2 + 3^2 + 3^2 = 16 + 9 + 9 = 34$
So Statement I false
Relation is reflexive, symmetric, transitive ⇒ equivalence
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