The number of relations, defined on the set $\{\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d}\}$, which are both reflexive and symmetric, is equal to:

JEE Main · 2026 · 21 Jan 2026 · Shift 1 · Sets Relations and Functions

The number of relations, defined on the set

{a, b, c, d}

, which are both reflexive and symmetric, is equal to:

Answer: (D)

A reflexive relation must contain all four diagonal pairs

(a, a), (b, b), (c, c), (d, d)

. Symmetry ties each off-diagonal ordered pair to its reverse, so the

(2 4) = 6

unordered off-diagonal pairs may each be included or excluded freely. This gives

2^{6} = 64

relations that are both reflexive and symmetric.

JEE Main · 2026 · 21 Jan 2026 · Shift 1 · Single correct option