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

Question

Accepted Answer

B. Let the set be

A = {𝑎, 𝑏, 𝑐, 𝑑},

so |A| = 4.

For a reflexive relation, all diagonal pairs

(𝑎,𝑎), (𝑏,𝑏), (𝑐,𝑐), (𝑑,𝑑)

must be included.

There are

4C2 = 6

unordered pairs of distinct elements.

For each unordered pair {𝑢, 𝑣}, symmetry gives two possibilities:

• Include both (𝑢, 𝑣) and (𝑣, 𝑢), or
• Exclude both.

Thus, each of the 6 unordered pairs has 2 independent choices.

Hence, the total number of reflexive and symmetric relations is

2⁶ = 64.