Functions Question 695
Let A and B be two finite sets having m and n elements respectively. Then, the total number of mappings from A to B is:
Options:
A) $ mn $
B) $ 2^{mn} $
C) $ m^{n} $
D) $ n^{m} $
Show Answer
Answer:
Correct Answer: D
Solution:
The image of any given element in A can be any one of the images of elements in B. $ \therefore $ The m elements in A can be assigned images $ n\times n\times\cdots\times n $ (m times) $ =n^{m} $ ways $ \therefore $ Total mapping from A to B $ =m^{n} $
BETA
