CBSE Class 12 maths Ncert Solutons Ex 1.1

 1) Determine whether each of the following relations are            reflexive, symmetric and transitive:

(ii) Relation R in the set N of natural numbers defined as
      R = {(x, y) : y = x + 5 and x < 4} 

Solution : 
Given that , 
A= { Set of all Natural numbers } 
x = 1 , 2, 3 
Y = x + 5 
If x = 1 , y = 1 + 5 = 6 => ( 1,6) 
If x = 2 , y = 2 + 5 = 7 => ( 2,7) 
If x = 3 , y = 3 + 5 = 8 => ( 3,8) 
∴ R = { ( 1,6) ( 2,7)  ( 3,8) }
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 , ( 1,6) ∈  R but ( 6,1) ∉ R 
so, it is not symmetric.
Transitive: 
Let ( a,b) ∈ R and ( b,c) ∈ R => ( a,c) ∈R 
since , ( 1,6) ∈R and ( 6, 9)∉R => (1,9) ∉ R
so , It is not transitive .
∴ Given R is neither reflexive nor symmetric and nor transitive .