If A is a set with m elements and n is a positive integer, the number of…
2025
If A is a set with m elements and n is a positive integer, the number of different elements in An is :
- A.
m * n
- B.
m * m
- C.
mn
- D.
nm
Attempted by 107 students.
Show answer & explanation
Correct answer: C
The set A^n denotes the Cartesian product of set A with itself n times. Since set A has m elements, the number of elements in the product is found by multiplying the cardinality of A, which is m, by itself n times. Thus, the total number of elements in A^n is m^n.