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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 relation
Correct answer is option 'A'. Can you explain this answer?
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Let A be a set of k (k>0) elements. Which is larger between the num...
For a set with k elements the number of binary relations should be 2(n*n) and the number of functions should be nn. Now, 2(n*n) => n2log (2) [taking log] and nn => nlog (n) [taking log]. It is known that n2log (2) > nlog (n). Hence, the number of binary relations > the number of functions i.e, Nr > Nf.
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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 relationsb)number of functionsc)the element setd)number of subsets of the relationCorrect answer is option 'A'. Can you explain this answer?
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