Let X=R × R. Define a relation R on X as: (a₁, b₁) R (a₂, b₂) b₁=b₂. Statement I: R is an equivalence relation. Statement II: For some (a, b) X, the set S=\(x, y) X: (x, y) R (a, b) represents a line parallel to y=x. In the light of the above statements, choose the correct answer from the options given below:

(B) Statement I is true but Statement II is false

(A) Both Statement I and Statement II are false

(C) Both Statement I and Statement II are true

(D) Statement I is false but Statement II is true

Sets, Relations and Functions: JEE Main 2025 Mathematics question

JEE Main 2025 · January, Unspecified (session-level dataset) · Q228

JEE Main 2025January, Unspecified (session-level dataset)MathematicsMediumSets, Relations and Functions168× since 2002

Let

\boldsymbol{X}=\mathbf{R} \times \mathbf{R}

. Define a relation

R

X

as:

\left(a_1, b_1\right) R \left(a_2, b_2\right) \Leftrightarrow b_1=b_2

. Statement I:

\mathbf{R}

is an equivalence relation. Statement II: For some

(a, b) \in X

, the set

S=\{(x, y) \in X : (x, y) R (a, b)\}

represents a line parallel to

y=x

. In the light of the above statements, choose the correct answer from the options given below:

JEE Main 2025 Sets, Relations and Functions Question with Solution (January Unspecified (session-level dataset), Q228) | JEE Arc