Let A = {p, q, r} . Which of following is an equivalence relation on A

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1.Relation and Function

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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

Solution

(d) Here $A = \{ p,\,q,\,r\} $

${R_1}$ is not symmetric because $(p,\,q) \in {R_1}$ but $(q,\,p) \notin {R_1}$

${R_2}$ is not symmetric because $(r,\,q)\, \in {R_2}$ but $(q,\,r)\, \notin {R_2}$

${R_3}$is not symmetric because $(p,\,q) \in {R_3}$ but $(q,\,p) \notin {R_3}$.

Hence, ${R_1},\,{R_2},\,{R_3}$ are not equivalence relation.

Standard 12

Mathematics

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