Functions Question 478
Question: Total number of equivalence relations defined in the set $ S={a,b,c} $ is:
Options:
5
3!
C) $ 2^{3} $
D) $ 3^{3} $
Show Answer
Answer:
Correct Answer: A
Solution:
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
