JEE Mains · Maths · STD 12 - 1. relation and function
Let \(A =\{0,1,2, \ldots 9)\). Let R be a relation on A defined by \(( x , y ) \in R\) if and only if \(| x - y |\) is a multiple of 3 .
Given below are two statements:
Statement I: \(n ( R )=36\)
Statement II: \(R\) is an equivalence relation.
In the light of the above statements, choose the correct answer from the options given below
- A Both Statement I and Statement II are correct
- B Statement I is incorrect but Statement II is correct
- C Statement I is correct but Statement II is incorrect
- D Both Statement I and Statement II are incorrect
Answer & Solution
Correct Answer
(B) Statement I is incorrect but Statement II is correct
Step-by-step Solution
Detailed explanation
Number of form \(3 K=4\) Number of form \(3 K+1=3\) Number of form \(3 K+2=4\) \(4 \times 4+3 \times 3+3 \times 3=34\) relations \(\Rightarrow x R y \Rightarrow y R x\) \(\Rightarrow( x - y )=3 \lambda,( y - z )=3 \mu\) \(\Rightarrow( x - z )=3(\lambda+\mu)\) \(R\) is reflexive,…
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