# 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:**

(b) Symmetric but neither reflexive nor transitive

**Solution:**

(c) Reflexive, symmetric and transitive.

**Solution:**

Question: 17 – Let R be relation defined on the set of natural number N as follows:
Find the domain and range of the relation R. Also, verify whether R is reflexive, symmetric and transitive.

**Solution:**

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:**

But this is an injective mapping.

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

**Solution:**

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

(c) a mapping from B to A

**Solution:**

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.
be the mapping defined by

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:**

This is onto but not one-one.

(iii) Which is neither one-one nor onto

**Solution:**

Here it is neither one-one nor onto.