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Many-One onto Function

Let E = 1, 2,...

Question

Let E = {1, 2, 3, 4} and F {1, 2}. Then the number of onto functions from E to F is

A

14

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B

16

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C

6

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D

4

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Solution

The correct option is A 14
The total number of functions are $2^{4} = 16$ . From the total number of functions, subtract those functions which do not have 2 as the range =1. Subtract those functions which do not have 1 as the range.
So, the answer is $16 - 2 = 14$

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Similar questions

E = {1, 2, 3, 4}

F = {1, 2}

then the number of onto functions from E to F is

Q. Let E = {1, 2, 3, 4} and F = {1, 2}. Then, the number of onto functions from E to F is

Q. Let A = {1, 2, 3, ...n} and B = {a, b}. Then the number of onto functions from A into B is

A = {1, 2, 3, 4}

B = {5, 7, 9}

, then the number of onto function from

A

B

Q. Assertion :Let

A = {x_{1}, x_{2}, x_{3}, x_{4}, x_{5}}

B = {y_{1}, y_{2}, y_{3}}

. The number of functions from

A

B

which are not onto is

45

Reason: The number of onto functions from

A

B

is equal to the coefficient of

x^{5}

5! (e^{x} - 1)^{3}

.

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