Question

If A = {1,2,3,4}; B = {a,b,c,d,e}
then the number of all possible constant functions from A to B is
(A) 9
(B) 4
(C) 5
(D) 6​

Answer 1

The number of all possible constant functions from A to B is 4.

Step 1: Find the number of possible function.

Given- A = {1,2,3,4} , B={a,b,c,d,e}

Possible relation from A to B will be

A                         B

1 --------------------> a

2 --------------------> b

3----------------------> c

4----------------------> d

                              e

Hence, there is only 4 possible constant function.

Answer 2

The number of all possible constant functions from A to B is 5 If A = {1,2,3,4}; B = {a,b,c,d,e}

Given

• A = {1,2,3,4}
• B = {a,b,c,d,e}

To Find:

• Number of all possible constant functions from A to B

Solution:

• Number of all possible constant functions from set A to set B  are equal to Cardinality of set B (number of elements in Set B)
• Constant function is a function whose output is fixed independent of input value  for example f(x) = c     where c is a constant

Step 1:

Count the number of elements in set B

B = {a,b,c,d,e}

n(B) = 5

Step 2:

Find   number of all possible constant functions from A to B

5  as Cardinality of set B is 5  (number of elements in Set B are 5)

f(x) = a , f(x) = b , f(x) = c , f(x) = d and f(x) = e , 5 possible constant functions from A to B

Correct option is C) 5

the number of all possible constant functions from A to B is 5