Question

Consider the set $A=3,4,5$ and the numbers of null relations, identity relation, universal relations, reflexive relations on $A$ are respectively $n_1,n_2,n_3$ and $n_4$ then the value of $n_1+n_2+n_3+n_4$ is equal to

• A. $8$
• B. $7$
• C. $73$
• D. $67$

Answer 1

The correct option is D $67$

Number of null set $n_1=0$

Number of identity relation $n_2=0$

Number of reflexive relations $n_3=2^{n^2-n}=2^{3^2-3}=2^6=64$

Number of universal relation $n_4=3$

Therefore,

$n_1+n_2+n_3+n_4=0+0+64+3$

$=67$