Let A = {1, 2} and B = {3, 4}. Find the number of relations from A to B. 16 32 64 108
Question
Let A = {1, 2} and B = {3, 4}. Find the number of relations from A to B. 16 32 64 108
Solution
A relation from set A to set B is a subset of the Cartesian product A x B.
The set A has 2 elements and the set B has 2 elements, so the Cartesian product A x B has 2*2 = 4 elements.
The number of subsets of a set with n elements is 2^n.
So, the number of relations from A to B is the number of subsets of the Cartesian product A x B, which is 2^4 = 16.
So, the answer is 16.
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