10 MCQs based on functions from A to B

If A has 4 elements and B has 5 elements, how many functions are there from A to B?

A) 20

B) 625

C) 1024

D) 120

Answer: B) 625

If A has 3 elements and B has 2 elements, how many one-to-one functions are there from A to B?

A) 0

B) 3

C) 6

D) 9

Answer: A) 0

If A has 5 elements and B has 5 elements, how many onto functions are there from A to B?

A) 0

B) 5

C) 25

D) 120

Answer: D) 120

If A has 6 elements and B has 4 elements, how many bijection functions are there from A to B?

A) 0

B) 4

C) 24

D) 360

Answer: A) 0

If A has m elements and B has n elements, what is the general formula for the number of functions from A to B?

A) nm

B) mn

C) n! / (n - m)!

D) m! / (m - n)!

Answer: A) nm

If A has m elements and B has n elements, what is the general formula for the number of one-to-one functions from A to B when m ≤ n?

A) nm

B) mn

C) n! / (n - m)!

D) m! / (m - n)!

Answer: C) n! / (n - m)!

If A has m elements and B has n elements, what is the general formula for the number of onto functions from A to B when m ≥ n?

A) nm

B) mn

C) ∑(-1)^k * C(n,k)*(n-k)^m , where k ranges from 0 to n

D) ∑(-1)^k * C(m,k)*(m-k)^n , where k ranges from 0 to m

Answer: C) ∑(-1)^k * C(n,k)*(n-k)^m , where k ranges from 0 to n

If A has m elements and B has n elements, what is the general formula for the number of bijection functions from A to B when m = n?

A) nm

B) mn

C) n! / (n - m)!

D) n!

Answer: D) n!

If A has 2 elements and B has 3 elements, how many functions are there from B to A?

A) 6

B) 8

C) 9

D) 12

Answer: D) 12

If A has 3 elements and B has 3 elements, how many bijection functions are there from A to B?

A) 3

B) 6

C) 9

D) None of these

Answer: B) 6 

 make short notes  for MCQ

The number of functions from A to B is equal to n^m, where n is the number of elements in B and m is the number of elements in A.
The number of one-to-one functions from A to B when m ≤ n is given by the formula n! / (n - m)!.
The number of onto functions from A to B when m ≥ n is given by the formula ∑(-1)^k * C(n,k)*(n-k)^m , where k ranges from 0 to n.
The number of bijection functions from A to B when m = n is equal to n!.
To find the number of functions from B to A, we need to switch the roles of A and B in the formula n^m, so we get m^n.
The number of bijection functions from A to B when m = n is equal to n!, which can be proved by counting the number of ways to arrange n elements in n slots.