CBSE Class 12 maths Ncert Solutons Ex 1.1

 1) (i) Determine whether each of the following relations are         reflexive, symetric and transitive:
(i) Relation R in the set A = {1, 2, 3, ..., 13, 14} defined as
     R = {(x, y) : 3x – y = 0}

Solution :

A = {1, 2, 3, ..., 13, 14}

 R = {(x, y) : 3x – y = 0}

3x-y=0

y=3x 

if x = 1 => y=3(1)=3 ==> ( 1,3) 

if x = 2 => y=3(2)=6 ==> ( 2,6) 

if x = 3 => y=3(3)=9 ==> ( 3,9)

if x = 4 => y=3(4)=12 ==> ( 4,12) 

if x = 5 => y=3(5)=15 ==> ( 5,15) 

here 15 is not in the set A , So ( 5, 15) is not possible.

R = { ( 1,3) ( 2,6) ( 3,9) ( 4,12) } 

Reflexive:
let a ∈ A => ( a,a) ∈ R 
Since 1 ∈ A => ( 1,1) ∉ A 
 so, It is not Reflexive.
Symmetric:
Let ( a,b)  ∈  R => ( b,a) ∈ R 
Since , ( 1,3) ∈  R but ( 3,1) ∉ R 
so, it is not symmetric.
Transitive: 
Let ( a,b) ∈ R and ( b,c) ∈ R => ( a,c) ∈R 
since , ( 1,3) ∈R and ( 3, 9) ∈ R => (1,9) ∉ R
so , It is not transitive .
∴ Given R is neither reflexive nor symmetric and nor transitive .