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

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.

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• Ex 1 (1)
• Ex 1 (2)
• Ex 1 (3)
• Ex 1 (4)
• Ex 1 (5)
• Ex 1 (6)
• Exmplr SA
• Exmplr LA(1)
• Exmplr LA(2)
• Exmplr LA(3)
• Exmplr LA(4)
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