Let a relation R on N × N be defined as: (x₁, y₁) R(x₂, y₂) if and only if x₁ ≤ x₂ or y₁ ≤ y₂. Consider the two statements: (I) R is reflexive but not symmetric. (II) R is transitive Then which one of the following is true?

(B) Both (I) and (II) are correct.

(C) Neither (I) nor (II) is correct.

Sets, Relations and Functions: JEE Main 2024 Mathematics question

JEE Main 2024 · 4 Apr, Evening shift · Q5395

JEE Main 20244 Apr, Evening shiftMathematicsMediumSets, Relations and Functions168× since 2002

Let a relation

\mathrm{R}

\mathrm{N} \times \mathbb{N}

be defined as:

\left(x_1, y_1\right) \mathrm{R}\left(x_2, y_2\right)

if and only if

x_1 \leq x_2

y_1 \leq 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?