Let X = ℝ × ℝ. Define a relation R on X as: (a₁, b₁) R (a₂, b₂) ⇔ b₁ = b₂. Statement-I: R is an equivalence re…

Question

Let $$X = \mathbb{R} 	imes \mathbb{R}$$. Define a relation $$R$$ on $$X$$ as:
$$ (a_1, b_1) \, R \, (a_2, b_2) \iff b_1 = b_2. $$
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 $$y = x$$.

Accepted Answer

B. Statement-I is true but Statement-II is false.

Answer

A. Statement-I is false but Statement-II is true.

Answer

C. Both Statement-I and Statement-II are true.

Answer

D. Both Statement-I and Statement-II are false.

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