Question

How to get total number of function

Answer 1

Number of functions from one set to another – Let X and Y are two sets having m and n elements respectively. In a function from X to Y, every element of X must be mapped to an element of Y. Therefore, each element of X has ‘n’ elements to be chosen from. Therefore, total number of functions will be n×n×n.. m times = n^m.

For example, X = {a, b, c} and Y = {4, 5}. A function from X to Y can be represented in Figure 1.

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