Let $A = \{p, q, r\}$. Which of the following is an equivalence relation on $A$
Let $A = \{p, q, r\}$. Which of the following is an equivalence relation on $A$
- A
${R_1}$ $= \{(p, q), (q, r), (p, r), (p, p)\}$
- B
${R_2}$ $= \{(r, q), (r, p), (r, r), (q, q)\}$
- C
${R_3}$ $= \{(p, p), (q, q), (r, r), (p, q)\}$
- D
None of these
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Consider the relations $R_1$ and $R_2$ defined as $a R_1 b$ $\Leftrightarrow a^2+b^2=1$ for all $a, b, \in R$ and $(a, b) R_2(c, d)$ $\Leftrightarrow a+d=b+c$ for all $(a, b),(c, d) \in N \times N$. Then
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- [JEE MAIN 2024]
Let $R$ be a relation on the set of all natural numbers given by $\alpha b \Leftrightarrow \alpha$ divides $b^2$.
Which of the following properties does $R$ satisfy?
$I.$ Reflexivity $II.$ Symmetry $III.$ Transitivity
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Which of the following properties does $R$ satisfy?
$I.$ Reflexivity $II.$ Symmetry $III.$ Transitivity
- [KVPY 2017]
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