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 =Number of function from set a to set b

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:

Number of function from set a to set b

Number of function from set a to set b

Number of function from set a to set b

Number of function from set a to set b

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 Number of function from set a to set b The number of functions from z (set of z elements) to e (set of 2xy elements) is Number of function from set a to set b 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:-
Number of function from set a to set b

Therefore, correct option is (d).

Do solve NCERT text book with the help of Entrancei NCERT solutions for class 12 Maths.

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