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Let A be a set of k (k>0) elements. Which is larger between the number of binary relations (say, Nr) on A and the number of functions (say, Nf) from A to A?(a) number of relations(b) number of functions(c) the element set(d) number of subsets of the relationI have been asked this question in an interview.The origin of the question is Types of Relations topic in portion Relations of Discrete Mathematics

Answer»

Right answer is (a) number of RELATIONS

Explanation: For a set with K elements the number of BINARY relations should be 2^(n*n) and the number of functions should be n^n. Now, 2^(n*n) => n^2log (2) [TAKING log] and n^n => nlog (n) [taking log]. It is known that n^2log (2) > nlog (n). Hence, the number of binary relations > the number of functions i.e, Nr > Nf.



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