Given two finite sets A and B such that n(A) = 2, n(B) = 3. Then total number of relations from A to B is
Question
Given two finite sets A and B such that
n(A) = 2, n(B) = 3.
Then total number of relations from A to B is
Solution
A relation from set A to set B is a subset of the Cartesian product A x B.
Step 1: Find the Cartesian product A x B. Since n(A) = 2 and n(B) = 3, the number of elements in A x B is n(A) * n(B) = 2 * 3 = 6.
Step 2: Each element in A x B can either be a part of the relation or not. So, for each of the 6 elements in A x B, there are 2 possibilities (either it is in the relation or it is not).
Step 3: Therefore, the total number of relations from A to B is 2^(number of elements in A x B) = 2^6 = 64.
So, there are 64 possible relations from set A to set B.
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