Let X=R \times R. Define a relation R on X as: (a_1, b_1) R (a_2, b_2) \Leftrightarrow b_1=b_2 Statement I: 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: [23 Jan 2025 Shift 2]

Correct Answer is : Statement I is true but Statement II is false

Statement I is true but Statement II is false

Statement I is false but Statement II is true

Both Statement I and Statement II are false

Both Statement I and Statement II are true

JEE Main 23 Jan 2025 Shift 2 Paper

Section: Mathematics

Question : 20 of 75

Marks: +1, -0

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:

[23 Jan 2025 Shift 2]

Statement I is true but Statement II is false
Statement I is false but Statement II is true
Both Statement I and Statement II are false
Both Statement I and Statement II are true

Validate

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