Functions Question 478
Question: Total number of equivalence relations defined in the set $ S={a,b,c} $ is:
Options:
A) 5
B) 3!
C) $ 2^{3} $
D) $ 3^{3} $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] The smallest equivalence relation is the identity relation $ R_1={(a,a),(b,b),(c,c) $ Then two ordered pairs of two distinct elements can be added to give three more equivalence relations $ R_2={(a,a),(b,b),(c,c),(a,b),(b,a)} $ Similarly $ R_3 $ and $ R_4. $ finally the largest equivalence relation i.e., the universal relation
BETA
