Mathematics Lab Activity-04 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 - 04

Objective

To demonstrate a function which is  one-one  but not 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 two nails on it . Name the nails on the strip as a, b as shown in figure 4.1

2. Paste another plastic strip on the right hand side of the cardboard and fix three nails on the plastic strip as shown in the figure 4.1. Name the nails on strip as 1, 2 and 3.

Figure 4.1

3. Join nails on the left strip to the nails on the right strip as shown in figure 4.2.

Figure 4.2

4. Take the set X = {a, b) and set Y = {1, 2, 3}. Join elements of set X to the elements of set Y as shown in fig.4.2

Observations

1. The image of the element a of set X in set Y is 2.

2. The image of the element b of set X in set Y is 3.

3. Different elements of set X have different images in set Y. So the function is one – one. One element {1} of set Y do not has their pre-image in set X. 

4. Range of the function is not equal to the co-domain. Hence this is not an onto function.

Result

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

Applications

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

VIVA – VOICE

Q1. A one one function crosses the horizontal line how many times ?

Ans. One time.

Q2. There exist more than one identity element for a set. True / False.

Ans. False. Identity element is unique for a set

Q3. What is the number of binary operations on a set having order n ?

Ans.  

Q4. How many functions from A to B can be composed, if A and B are two non-empty sets containig m and n elements respectively ?

Ans. n^m

Q5.  How many one one functions from A to B can be composed, if A and B are two non-empty sets containig m and n elements respectively ?

Ans. ⁿP_m 

Q6. What is the number of relations from A toB, if n(A) = m and n(B) = n ?

Ans.  2^mn    

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