JAMIA 2024 — Mathematics PYQ

Solution:

Diya gaya set:

Yahan elements ki sankhya $n=3$ hai.

Equivalence relations ki sankhya nikalne ke liye hum Bell Number ($B_n$) ka use karte hain:

1. Case 1: $n=0$

   $$B_0=1$$

2. Case 2: $n=1$ (Set {1})

   $$B_1=1$$

3. Case 3: $n=2$ (Set {1, 2})

   $$B_2=2$$

   (Partitions: $\{\{1,2\}\},\{\{1\},\{2\}\}$)

4. Case 4: $n=3$ (Set {1, 2, 3})

   $$B_3=5$$

Possible Partitions for $n=3$:

• $\{\{1,2,3\}\}$ — (1 relation)

• $\{\{1,2\},\{3\}\}$ — (1 relation)

• $\{\{1,3\},\{2\}\}$ — (1 relation)

• $\{\{2,3\},\{1\}\}$ — (1 relation)

• $\{\{1\},\{2\},\{3\}\}$ — (1 relation)

Total Relations:

Final Answer:

Maximum number of equivalence relations on set $A=\{1,2,3\}$ is 5.