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Algebra
Relations, Reflexive and Symmetric Relations
jee_main_2026_jan_21_shift_1
Grade None
Question:
The number of relations, defined on the set {a, b, c, d} which are both reflexive and symmetric, is equal to:
A. 256
B. 16
C. 1024
D. 64
Step-by-Step Solution
Key Concept: For reflexive relations, all diagonal elements must be present.
Step 1: Reflexive requires 4 diagonal elements: (a,a),(b,b),(c,c),(d,d) — all fixed. Step 2: For symmetric relations, for each of the 6 unordered pairs, 2 choices: include both or include neither. Step 3: Total = 2⁶ = 64.
Correct Answer:D
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