Problem 4 Solution

This page contains the NCERT mathematics class 12 chapter Relations and Functions Exercise 1.1 Problem 4 Solution. Solutions for other problems are available at Exercise 1.1 Solutions

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Exercise 1.1 Problem 4 Solution

4. Show that the relation R in R defined as R =

(a, b) : a \le b

, is reflexive and transitive but not symmetric.

To Check whether R is Reflexive: The relation R in the set A is reflexive if

(a, a)

∈ R, for every

a

∈ A.

As every element

a

is equal to itself, it satisfies the condition

{a \le a}

⇒

(a, a)

∈ R

∴ R is Reflexive

To Check whether R is Symmetric: The relation R in the set A is symmetric if

(a_1, a_2)

∈ R implies that

(a_2, a_1)

∈ R, for all

a_1, a_2

∈ A

We have 2 ≤ 4. But

4 \nleq 2

(4 > 2). Thus for many elements when

(a, b)

∈ R, we have

(b, a)

≠ R.

∴ R is not symmetric.

To Check whether R is Transitive: The relation R in the set A is transitive if

(a_1, a_2)

∈ R and

(a_2, a_3)

∈ R implies that

(a_1, a_3)

∈ R, for all

a_1, a_2, a_3

∈ A

When

{a \le b}

and

{b \le c}

then we always have

{a \le c}

∴ R is Transitive

∴ R is both reflexive and transitive but not symmetric

Back to Exercise 1.1

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