Mathematics Lab Activity-03 Class XII

        Mathematics Lab Activity-3 Class XII

Mathematics Laboratory Activities on Relations & Functions for class XI Non-Medical students with complete observation tables strictly according to the CBSE syllabus.

Chapter - 01 | relations & functions

Activity - 03

Objective

To demonstrate a function which is not one-one  but is onto.

Material Required

Cardboard, nails, strings, adhesive and plastic strips.

Procedure

1. Take a cardboard and paste a plastic strip on the left hand side of the cardboard and fix three nails on it as shown in figure 3.1. Name the nails on the strip as 1, 2, 3.

Figure 3.1

2. Paste another plastic strip on the right hand side of the cardboard and fix two nails on the plastic strip as shown in the figure 3.1. Name the nails on strip as a and b.
3. Join nails on the left strip to the nails on the right strip as shown in figure 3.2.
4. Take the set X = {1, 2, 3) and set Y = {a, b}.

Figure 3.2

5. Join elements of set X to the elements of set Y as shown in fig.3.2

Observations

1. The image of the element 1 of set X in set Y is a.

2. The image of the element 2 of set X in set Y is b.
3. The image of the element 3 of set X in set Y is b.
4. Two elements {2, 3} of set X have same image b in set Y. So the function is not one – one. This is a many one function.
5. Every element of set Y has their pre-image in set X. Range of the function is equal to the co-domain. Hence this is an onto function.

Result

The function given above is an onto function and is not one-one function.

Applications

This activity is used to explain the concept of one-one and onto function.

VIVA – VOICE

Q. 1 Is the relation given below is a function ?

{ (2, 1), (5, 1), (8, 1), (11, 1), (14, 1), (17, 1)

Ans. No two ordered pair have the same first element so it is a function. Also different elements have same image so it is a many one relation.

Q2. For a function f: A →B, an onto function, If n(B) ........... n(A).

Ans. Less than or equal to.

Q3. If A = {1, 2, 3}, B = {4, 5} and f = {(1, 4), (1, 5), (2, 4), (3, 5)}. Is f a function from A to B ?

Ans. No, because two ordered pair (1, 4) and (1, 5) have the same first element.

Q4. What is the range of the function   ?

Ans. Range is {-1,1}

Q5. Find the number of one-one functions for two sets A and B, where O(A) = 2 and O(B) = 3.

Ans. No. of one one function = ³P₂ = 6

Q6. Define onto function ?

Ans. A function f:A⟶B is said to be an onto function if range of f is equal to B

Q7. Find the number of bijective functions from A to B.

(i) n(A) = 3, n(B) = 2

(ii) n(A) = n(B) = 4

Ans. (i) There is no bijective function because for bijective function n(A) = n(B)

        (ii) No. of bijective functions = 4! = 24

Q8. If A = {1,2,3}, how many functions from A to A are possible ?

Ans. 3^3 = 27

Q9. If f:A⟶B is an injective function such that range of f = {1, 2}, find the number of elements in A

Ans. Two elements

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