JEE Mains · Maths · STD 12 - 1. relation and function
Let a relation \(R\) on \(\mathbb{N} \times \mathbb{N}\) be defined as : \(\left(\mathrm{x}_1, \mathrm{y}_1\right) \mathrm{R}\left(\mathrm{x}_2, \mathrm{y}_2\right)\) if and only if \(\mathrm{x}_1 \leq \mathrm{x}_2\) or \(\mathrm{y}_1 \leq \mathrm{y}_2\) Consider the two statements : (\(I\)) \(\mathrm{R}\) is reflexive but not symmetric. (\(II\)) \(\mathrm{R}\) is transitive Then which one of the following is true?
- A Only (\(II\)) is correct.
- B Only (\(I\)) is correct.
- C Both (\(I\)) and (\(II\)) are correct.
- D Neither (\(I\)) nor (\(II\)) is correct.
Answer & Solution
Correct Answer
(B) Only (\(I\)) is correct.
Step-by-step Solution
Detailed explanation
All \(\left(\left(\mathrm{x}_1 \mathrm{y}_1\right),\left(\mathrm{x}_1, \mathrm{y}_1\right)\right)\) are in \(\mathrm{R}\) where \(\mathrm{x}_1, \mathrm{y}_1 \in \mathrm{N} \therefore \mathrm{R}\) is reflexive \(((1,1),(2,3)) \in \mathrm{R}\) but…
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