Functions Question 453
Question: Let $A=\{p, q, r\}$. Which of the following is an equivalence relation on $A$ ?
Options:
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
Show Answer
Answer:
Correct Answer: D
Solution:
[d] $ R_1 $ is not reflexive, because $ (q,q)(r,r)\notin R_1. $
$ \therefore R_1 $ is not an equivalence relation $ R_2 $ is not reflexive, because $ (p,p)\notin R_2. $
$ \therefore R_2 $ is not an equivalence relation. $ R_3 $ is reflexive, because $ (p,p),(q,q),(r,r)\in R_3. $ $ R_3 $ is not symmetric, because $ (p,q)\in R_3 $ but $ (q,p)\notin R_3. $
BETA
