If f: A → B is a function and |A| = 5, |B| = 3, what is the maximum number of distinct functions that can be formed?
Practice Questions
1 question
Q1
If f: A → B is a function and |A| = 5, |B| = 3, what is the maximum number of distinct functions that can be formed?
3^5
5^3
15
8
The maximum number of distinct functions is |B|^|A| = 3^5 = 243.
Questions & Step-by-step Solutions
1 item
Q
Q: If f: A → B is a function and |A| = 5, |B| = 3, what is the maximum number of distinct functions that can be formed?
Solution: The maximum number of distinct functions is |B|^|A| = 3^5 = 243.
Steps: 6
Step 1: Understand what a function is. A function f: A → B means that every element in set A is assigned to exactly one element in set B.
Step 2: Identify the sizes of the sets. Here, |A| = 5 means there are 5 elements in set A, and |B| = 3 means there are 3 elements in set B.
Step 3: Realize that for each element in set A, you can choose any of the elements in set B. Since there are 3 choices in B for each of the 5 elements in A, you will multiply the choices.
Step 4: Calculate the total number of distinct functions. Since each of the 5 elements in A can map to any of the 3 elements in B, the total number of functions is 3 (choices for the first element) multiplied by 3 (choices for the second element) multiplied by 3 (choices for the third element) multiplied by 3 (choices for the fourth element) multiplied by 3 (choices for the fifth element). This is the same as 3 raised to the power of 5.
