Sets & Relations
Equivalence Relations
MMTS_Full_Test_06
Grade 12
Question:
Let $R_1$ and $R_2$ be two relations defined on $\mathbb{R}$ by $aR_1b\Leftrightarrow ab\ge 0$ and $aR_2b\Leftrightarrow a\ge b$. Then
$R_1$ is an equivalence relation but not $R_2$
$R_2$ is an equivalence relation but not $R_1$
Both $R_1$ and $R_2$ are equivalence relations
Neither $R_1$ nor $R_2$ is an equivalence relation
Step-by-Step Solution
Key Concept: Check reflexive, symmetric, transitive for each
$R_1$: not transitive. $R_2$: not symmetric. Neither is equivalence.
Correct Answer: 4