Relations
Counting Relations
JEE Main 2024
Grade 11
Question:
The number of symmetric relations on $\{1, 2, 3, 4\}$ which are not reflexive is _____.
Step-by-Step Solution
Key Concept: Total symmetric relations on a 4-element set: $2^{4(4+1)/2} = 2^{10} = 1024$. Reflexive symmetric relations: all 4 diagonal pairs fixed, 6 off-diagonal pairs free $\Rightarrow 2^6 = 64$. Non-reflexive symmetric $= 1024 - 64 = 960$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: 960