JEE Mains · Maths · STD 12 - 1. relation and function
Let \(A=\{0,1,2,3,4,5\}\). Let \(R\) be a relation on A defined by \((x, y) \in R\) if and only if max \(\{x, y\} \in\{3,4\}\). Then among the statements \(\left(\mathrm{S}_1\right)\) : The number of elements in R is 18 , and \(\left(\mathrm{S}_2\right)\) : The relation R is symmetric but neither reflexive nor transitive
- A both are true
- B both are false
- C only \(\left(\mathrm{S}_2\right)\) is true
- D only \(\left(\mathrm{S}_1\right)\) is true
Answer & Solution
Correct Answer
(C) only \(\left(\mathrm{S}_2\right)\) is true
Step-by-step Solution
Detailed explanation
\(A=\{0,1,2,3,4,5\}\) \(\mathrm{R} \equiv\{(0,3),(3,0),(0,4),(4,0),(1,3),(3,1),(1,4)\), \((4,1),(2,3),(3,2),(2,4),(4,2),(3,3),(3,4),(4,3)\), \((4,4)\}\) Total 16 elements Not reflexive as \((0,0), \ldots \ldots,(2,2) \notin \mathrm{R}\) Symmetric \(\because \forall\) all a,b…
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