JAMIA 2021 — Mathematics PYQ
JAMIA | Mathematics | 2021The maximum number of equivalence relations on the set A=1,2,3 are:
Choose the correct answer:
- A.
1
- B.
2
- C.
3
- D.
5
(Correct Answer)
5
Explanation
-
Case 1: All elements in 1 subset
{{1,2,3}}(1 partition)
-
Case 2: Partitioned into 2 subsets (2+1)
{{1,2},{3}}{{1,3},{2}}{{2,3},{1}}(3 partitions)
-
Case 3: Partitioned into 3 subsets (1+1+1)
{{1},{2},{3}}(1 partition)
Calculation
Total number of equivalence relations=1+3+1
Total=5
Alternatively, using Bell Numbers (Bn):
B0=1
B1=1
B2=2
B3=5
Final Answer:
The maximum number of equivalence relations is 5.
Explanation
-
Case 1: All elements in 1 subset
{{1,2,3}}(1 partition)
-
Case 2: Partitioned into 2 subsets (2+1)
{{1,2},{3}}{{1,3},{2}}{{2,3},{1}}(3 partitions)
-
Case 3: Partitioned into 3 subsets (1+1+1)
{{1},{2},{3}}(1 partition)
Calculation
Total number of equivalence relations=1+3+1
Total=5
Alternatively, using Bell Numbers (Bn):
B0=1
B1=1
B2=2
B3=5
Final Answer:
The maximum number of equivalence relations is 5.