Sets, Relations & Functions
Reflexive and Symmetric Relations — Counting
nta_pyq_2026_jan
Grade None
Question:
The number of relations, defined on the set $\{a,b,c,d\}$, which are both reflexive and symmetric, is equal to:
Step-by-Step Solution
Key Concept: For $n=4$: reflexive means 4 diagonal pairs fixed. Remaining off-diagonal pairs: $\binom{4}{2}=6$ unordered pairs. For symmetry, each pair $\{x,y\}$ is either included (both $(x,y)$ and $(y,x)$) or excluded: 2 choices each.
64 relations.
Correct Answer: 3