Question

If the number of relations on a finite set A having ‘n’ elements is 2^16, then n=

Answer 1

Answer:

if no. of elements in a set A be n and no. of elements in another set B = m, then no. of elements in the cartesisn product of A & B i.e. A× B = n × m . Therefore no. of subsets of A× B is 2^(mn) = no. of relations that can be described from A to B . Here no. of elements in the set A is given to be equal to = n, therefore no. of relations on A(or relations from A to A) = 2^(n^2) = 2^(16) (given) ==> n^2 = 16 ==> n = 4

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