Question

Let $R$ be the set of all binary relations on the set $\{1,2,3\}$. Suppose a relation is chosen from $R$ at random. The probability that the chosen relation is reflexive (round off to 3 decimal places) is

• A. 0.125

Answer 1

The correct option is A 0.125
$A=\{1,2,3\}$
$n=|A|=3$
Number of relations on $A=2^{n^2}=2^{3^2}=2^9$
Number reflexive relations on $A$
$=2^{n^2-n}=2^{3^2-3}=2^6$
$P$(reflexive relation) $=\frac{2^6}{2^9}=\frac{1}{8}=0.125$