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JEE Main 20244 AprilEvening Shift
Exam
JEE Main
Year
2024
Date
4 April
Shift
Evening Shift
Subject
Mathematics
Chapter
Sets and Relations

JEE Main 2024 · 4 April · Evening Shift · Mathematics · Sets and Relations

Let a relation R on N × N be defined as: (x_1, y_1) R(x_2, y_2) if...

Let a relation R\mathrm{R} on N×N\mathrm{N} \times N be defined as: \left(x_1, y_1\right) \mathrm{R}\left(x_2, y_2\right) if and only if x1≤x2x_1 \leq x_2 or y1≤y2y_1 \leq y_2. Consider the two statements: (I) R\mathrm{R} is reflexive but not symmetric. (II) RR is transitive. Then which one of the following is true?

Options

  1. ABoth (I) and (II) are correct.
  2. BOnly (II) is correct.
  3. CNeither (I) nor (II) is correct.
  4. DOnly (I) is correct.

Correct answer

D. Only (I) is correct.

Step-by-step solution

All \left(\left(\mathrm{x}_1 \mathrm{y}_1\right),\left(\mathrm{x}_1, \mathrm{y}_1\right)\right) are in R\mathrm{R} where x1,y1∈N∴R\mathrm{x}_1, \mathrm{y}_1 \in \mathrm{N} \therefore \mathrm{R} is reflexive ((1,1),(2,3))∈R but ((2,3),(1,1))∉R((1,1),(2,3)) \in \mathrm{R} \text{ but }((2,3),(1,1)) \notin \mathrm{R} ∴R\therefore \mathrm{R} is not symmetric ((2,4),(3,3))∈R((2,4),(3,3)) \in \mathrm{R} and ((3,3),(1,3))∈R((3,3),(1,3)) \in \mathrm{R} but ((2,4)((2,4), (1,3))∉R(1,3)) \notin \mathrm{R} ∴R\therefore \mathrm{R} is not transitive
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