# Relation and Function

## NCERT Solution

### Exercise 1.1 Part 3

Question 2: Show that the relation in the set R of real number, defined as
Is neither reflexive nor symmetric nor transitive.

**Solution:**

But this relation is contradictory, and hence false

Thus, R is not reflexive

This relation is also not possible and hence false

Thus, R is not symmetric

This relation is also false

Thus, R is not transitive

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

Question 3: Check whether the relation R defined in the set {1, 2, 3, 4, 5, 6} as R = {(a,b) : b = a + 1} is reflexive, symmetric or transitive.

**Solution:**

Let A = {1, 2, 3, 4, 5, 6}

A relation R is defined on set A as:

R = {(a,b) : b = a + 1}

Thus, R = {(1, 2), (2, 3), (3, 4), (4, 5), (5, 6)}

Thus, R is not reflexive relation

Again,(1,2)∈R but (2,1)∉R

Thus, R is not symmetric

Now,again,(3,4)∈R and (4,5)∈R

But,(3,5)∉R

Thus, R is not transitive.

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

Question 4: Show that the relation R in R defined as
is reflexive and transitive but not symmetric.

**Solution:**

Thus, R is reflexive relation

Thus, R is not symmetric

Thus, R is transitive.

Therefore, R is reflexive and transitive but not symmetric.

Question 5: Check whether the relation R in R defined by
is reflexive, symmetric or transitive.

**Solution:**

Thus, R is not reflexive

Thus, R is not symmetric

Thus, R is not transitive.

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