UPSC NDA I 2019 Mathematics Solved Paper

(D)
X = {1,2,3, 4}
R= {(1,1) ,(2,2) , (3,3 )(1, 2) , (2,1) (2,3) ,(3,2)}
(i) Reflexivity
R is reflexive if xRx for all x ∈ X
But (4,4) ∉ R ⇒ R is not reflexive
(ii) Transitivity
R is transitive if xRy , yRz ⇒ xRz ∀ x , y ,z∈ R
But (1,2),(2,3)∈ R and (1,3)∉R
⇒ R is not transitive
(iii) Symmetry
R is symmetric if xRy ⇒ yRx ∀ x , y ∈R which is true for given relation