Question

Let S be a set of n>0 elements. Let  be the number Br of binary relations on S and let Bf be the number of functions from S to S. The expression for Br and Bf, in terms of n should be ____________

(a) n^2 and 2(n+1)^2

(b) n^3  and n^(n+1)

(c) n and n^(n+6)

(d) 2^(n*n)  and n^n

I have been asked this question in an interview for internship.

I would like to ask this question from Types of Relations topic in portion Relations of Discrete Mathematics

Answer 1

Correct option is (d) 2^(n*n)  and n^n

Best explanation: For a set with n elements the number of binary relations should be 2^(n*n) and the number of functions should be n^n. Hence Br = 2^(n*n)  and Bf = n^n.