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COMEDK2023Morning ShiftMathematicsSets and RelationsActual

If n(A)=p and n(B)=q , then the numbers of relations from the set A to the set B is

Options

  1. A2^ p q
  2. Bp+q
  3. Cp q
  4. D2^ p+q

Correct answer

A. 2^ p q

Step-by-step solution

A relation from set A to set B is defined as a subset of the Cartesian product A B . The number of elements in the Cartesian product A B is given by n(A B) = n(A) n(B) = p q = pq . The total number of subsets of a set with n elements is 2^n . Therefore, the total number of relations from set A to set B is the number of subsets of A B , which is 2^ pq . Answer: 2^ p q

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