This set of Discrete Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Number of Functions”.

1. An injection is a function which is :

a) many-one

b) one-one

c) onto

d) none of the mentioned

View Answer

Explanation: One-One functions are also known as injection.

2. A mapping f : X -> Y is one one if :

a) f(x_{1}) ≠ f(x_{2}) for all x_{1}, x_{2} in X.

b) If f(x_{1}) = f(x_{2}) then x_{1} = x_{2} for all x_{1}, x_{2} in X.

c) f(x_{1}) = f(x_{2}) for all x_{1}, x_{2} in X.

d) None of the mentioned

View Answer

Explanation: In one one function every element in A should have unique image in B,thus if two image are equal this means there preimages are same.

3. A function is defined by mapping f : A -> B such that A contains m elements and B contains n elements and m ≤ n then number of one one functions are :

a) ^{n}C_{m} x m!

b) ^{n}C_{m} x n!

c) 0

d) none of the mentioned

View Answer

Explanation: From n elements in B we need to select m elements and then arrange them in all ways, thus answer=

^{n}C

_{m}x m!.

4. A function is defined by mapping f : A -> B such that A contains m elements and B contains n elements and m>n then number of one one functions are :

a) ^{n}C_{m} x m!

b) ^{n}C_{m} x n!

c) 0

d) none of the mentioned

View Answer

Explanation: Since for function to be defined every element should have a image , since m > n atleast one element need to have same image, thus we can’t form any unique images and hence the number of one one function are zero.

5. State whether the given statement is true or false

For an onto function range is equivalent to codomain.

a) True

b) False

View Answer

Explanation: Since in onto function every image should have preimage thus all the elements in codomain should have preimages.

6. State whether the given statement is true or false

Onto function are known as injection.

a) True

b) False

View Answer

Explanation: Onto functions are known as surjection.

7. Set A has 3 elements and set B has 4 elements then number of injections defined from A to B are?

a) 12

b) 24

c) 36

d) 48

View Answer

Explanation:Injections will be

^{4}C

_{3}x 3!=24.

8. A function is defined by mapping f : A -> B such that A contains m elements and B contains n elements and 1≤n≤m then number of onto functions are:

a) _{r=1}∑^{r=n} ^{n}C_{r} (-1)^{n-r} r^{m}

b) _{r=1}∑^{r=n} ^{n}C_{r} (-1)^{n-r} r^{n}

c) _{r=1}∑^{r=n} ^{n}C_{r} (-1)^{m-r} r^{n}

d) None of the mentioned

View Answer

Explanation: The number of onto function is equal tpo the coffecient of x

^{m}in m!(e

^{x}– 1)n.

9. A function is defined by mapping f:A->B such that A contains m elements and B contains n elements and m > n then number of bijections are :

a) ^{n}C_{m} x m!

b) ^{n}C_{m} x n!

c) 0

d) none of the mentioned

View Answer

Explanation: Since we can’t define any one one function in such case so number of bujections will be zero.

10. State True or False.

A bijection is a function which is many-one and onto.

a) True

b) False

View Answer

Explanation: A bijection is a function which is one-one(injection) and onto(surjection).

**Sanfoundry Global Education & Learning Series – Discrete Mathematics.**

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