Question

The number of reflexive relation in set A = {a, b, c} is equal to

• A. $2^9$
• B. $2^4$
• C. $2^7$
• D. $2^6$

Answer 1

The correct option is D $2^6$

$\therefore$ Total number of relation in set A $2^{3\times 3}=2^9$

and maximum number of cartesian product = 9 out of which 3 ordered pair is necessary for reflexive.

So, for remaining 6 ordered pair

Number of ordered pair required.${=}^6{C}_0+{}^6{C}_1+{}^6{C}_2+.....{.}^6{C}_6$ =$2^6$