Let E = {1, 2, 3, 4} and F = {1, 2}. Then the number of onto functions from E to F is [2001]

Question

Let $E$ = {1, 2, 3, 4} and $F$ = {1, 2}. Then the number of onto functions from $E$ to $F$ is [2001]

Smart Achievers · Accepted Answer

(1)

E = {1, 2, 3, 4} and F = {1, 2}

From E to F we can define, in all, 2 × 2 × 2 × 2 = 16 functions (2 options for each element of E), out of which 2 are into, when all the elements of E either map to 1 or to 2.

$∴$ Number of onto functions = 16 − 2 = 14

Solution

Q.
Let $E$ = {1, 2, 3, 4} and $F$ = {1, 2}. Then the number of onto functions from $E$ to $F$ is [2001]

1 14

2 16

3 12

4 8

Ans.
(1)

E = {1, 2, 3, 4} and F = {1, 2}

From E to F we can define, in all, 2 × 2 × 2 × 2 = 16 functions (2 options for each element of E), out of which 2 are into, when all the elements of E either map to 1 or to 2.

$∴$ Number of onto functions = 16 − 2 = 14

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