CBSE Class 12 maths Ncert Solutons Ex 1.1

1) Determine whether each of the following relations are reflexive,     symmetric and transitive:
(iii) Relation R in the set A = {1, 2, 3, 4, 5, 6} as 

R = {(x, y) : y is divisible by x}

Solution: 

Given taht h   A = {1, 2, 3, 4, 5, 6}
let a ∈ A => ( a,a) ∈ R 
Since 1 ∈ A => ( 1,1) ∈A 
1 is divisible by 1 ( ∵ any number divisible by it self)
so, It is Reflexive.
Symmetric:
Let ( a,b)  ∈  R => ( b,a) ∈ R 
Since , 
2 is divisible by 1

=>( 1,2) ∈  R 

1 is not divisible by 2
=> ( 2,1) ∉ R 
so, it is not symmetric.
Transitive: 
Let ( a,b) ∈ R and ( b,c) ∈ R => ( a,c) ∈R 
since , 2 is divisible by 1 
( 1,2) ∈ R 
and  4 is divisible by 2 
( 2,4 ) ∈ R 
=> 4 is divisible by 1 
=> ( 1,4) ∈R
so , It is transitive .
∴ Given R is  reflexive and transitive but not symmetric.