Class 12 Maths

Relation and Function

NCERT Exemplar Problem

Long Answer Type Part 1

Question 16: If A = {1, 2, 3, 4}, define relations on A which have properties of being

(a) Reflexive, transitive but not symmetric

Solution:

NCERT Exemplar Problems and Solution class 12 Math (16)

(b) Symmetric but neither reflexive nor transitive

Solution:

NCERT Exemplar Problems and Solution class 12 Math (17)

(c) Reflexive, symmetric and transitive.

Solution:

NCERT Exemplar Problems and Solution class 12 Math (18)

Question: 17 – Let R be relation defined on the set of natural number N as follows: NCERT Exemplar Problems and Solution class 12 Math (19) Find the domain and range of the relation R. Also, verify whether R is reflexive, symmetric and transitive.

Solution:

NCERT Exemplar Problems and Solution class 12 Math (20)
NCERT Exemplar Problems and Solution class 12 Math (21)

Thus, R is neither reflexive, nor symmetric and nor transitive.

Question – 18 – Given A {2, 3, 4}, B = {2, 5, 6, 7}. Construct an example of each of the following:

(a) an injective mapping from A to B

Solution:

NCERT Exemplar Problems and Solution class 12 Math (22)

But this is an injective mapping.

(b) a mapping from A to B which is not injective

Solution:

NCERT Exemplar Problems and Solution class 12 Math (23)

Here it is clear that it is not an injective mapping.

(c) a mapping from B to A

Solution:

NCERT Exemplar Problems and Solution class 12 Math (24)

Here it is clear that every first component is from B and second component is from A, thus h is a mapping from B to A.



Question – 19: Give an example

(i) Which is one-one but not onto

Solution:

Let A be the set of all 100 students in a school in a particular class say ninth. NCERT Exemplar Problems and Solution class 12 Math (25) be the mapping defined by NCERT Exemplar Problems and Solution class 12 Math (26)

Here it is clear that f is one-one because no two students of the same class can have the same roll number.

Let roll number of student start from 1 and ends on 100.

This implies that 101 in N is not the roll number of any of the student of the class, so that 101 is not an image of any element of A under f.

Therefore, f is not onto.

(ii) Which is not one-one but onto

Solution:

NCERT Exemplar Problems and Solution class 12 Math (27)

This is onto but not one-one.

(iii) Which is neither one-one nor onto

Solution:

NCERT Exemplar Problems and Solution class 12 Math (28)

Here it is neither one-one nor onto.



Exercise 1

Exemplar Problems