Maths · Relations, type of relations, equivalence relations
Let and What is the number of distinct relations from to ?
Let \( A=\{x, y, z\} \) and \( B=\{p, q, r, s\} \) What is the number of distinct relations from \( \boldsymbol{B} \) to \( \boldsymbol{A} \) ?
- A. 4096
- B. 4094
- C. 128
- D. 126
Step-by-step solution
A relation from B to A is a subset of the Cartesian product B × A. B has 4 elements, A has 3 elements, so B × A has 4×3 = 12 elements. The number of subsets of a set with 12 elements is 2^12 = 4096. Hence, there are 4096 distinct relations.
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