Question

The number of reflexive relations on a set with four elements is equal to

• A. 2048
• B. 4096
• C. 256
• D. 8192

Answer 1

The correct option is B 4096

Total no. of elements in the set=4.
Total No. of relations = $2^{4\times 4}=2^{16}$
In cartesian product, we have 16 ordered pairs in which 4 are compulsory for reflexive relation.
Out of the remaining 12 ordered pairs, we can take
$12C0+12C1+12C2+.....+12C12=2^{12}=4096$