Let \(A = \{1, 2, 3, 4\}\). The number of relations on A that are both reflexive and symmetric is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 64
\(A \times A\) has 16 ordered pairs: 4 pairs of the form (a, a) and 12 pairs (a, b) with \(a \ne b\).
Reflexive: all 4 pairs (1, 1), (2, 2), (3, 3), (4, 4) must be present, so there is no choice for them.
Symmetric: the 12 other pairs fall into 6 couples \(\{(a, b), (b, a)\}\); each couple is either taken whole or left out.
number of couples \(= \displaystyle\frac{12}{2} = 6\)
number of relations \(= 2^{6} = 64\)