Source: Extra Practice
If a set A contains 3 elements and set B contains 4 elements, how many relations can be defined from set A to set B?
Options
Option A
12
Option B
2^7
Option C is correct
2^12
Option D
4^3
Explanation
A relation from A to B is any subset of the Cartesian product A × B. The number of elements in A × B is n(A) × n(B) = 3 × 4 = 12. The number of subsets of a set with n elements is 2^n. Therefore, the number of relations is 2^12. Option A (12) is just the number of elements in the product, not the number of subsets. Option B (2^7) incorrectly adds the number of elements instead of multiplying them. Option D (4^3) is the number of functions from A to B, not relations.