# Number of function from set a to set b

#### Math Formulas

## Number of function from set a to set b

**Definition :-**

A function f from a set A to a set B is a relation between A and B which satisfies two properties:

- 1. every element in A is related to some element in B, and
- 2. no element in A is related to more than one element in B.
- In other words, given any element a∈ A, there is a unique element b∈ B with(a, b)∈ f.

**Note:** The digraph of a relation which is a function has exactly one arrow leaving each point in the set A. The matrix of a relation which is a function has exactly one T in each row.

**Formula description :-**

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. T

The total number of functions will be n×n×n.. M times =

**Example 1 :-**let x, y, z be sets of sizes x, y and z respectively. Let w = x x y. Let e be the set of all subsets of w. The number of functions from z to e is:

**Solution :-**

As w = x x y is given, number of elements in w is xy. As e is the set of all subsets of w, number of elements in e is The number of functions from z (set of z elements) to e (set of 2xy elements) is So the correct option is (d)

**Example 2 :-** let s denote the set of all functions f: {0,1}4 → {0,1}.Denote by n the number of functions from s to the set {0,1}. The value of log2log2n is ______.

(a) 12

(b) 13

(c) 15

(d) 16

**Solution:-**

Therefore, correct option is (d).

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