The problem asks to find the number of functions from set A to set B, and from set B to set A, given the cardinality (number of elements) of each set. We are given $|A| = 4$ and $|B| = 5$.

1. Problem Description

The problem asks to find the number of functions from set A to set B, and from set B to set A, given the cardinality (number of elements) of each set. We are given $|A| = 4$ and $|B| = 5$.

2. Solution Steps

i) The number of functions from A to B is given by the formula:

$|B|^{|A|}$

Substituting the given values, we get:

$5^4 = 5 \times 5 \times 5 \times 5 = 625$

ii) The number of functions from B to A is given by the formula:

$|A|^{|B|}$

Substituting the given values, we get:

$4^5 = 4 \times 4 \times 4 \times 4 \times 4 = 1024$

3. Final Answer

i) The number of functions from A to B is

6

2

5. ii) The number of functions from B to A is 1024.