Match List I with List II.

Choose the correct answer from the options given below :

A - IV, B - I, C - III, D - II

A. R = {(x, y) : x, y ∈ same school} 

so (x, x) ∈ R  for every x ∈ A          →     IV

(x, y) ∈ R ⇒ (y, x) ∈ R

(x, y) ∈ R  ,  (y, z) ∈ R ⇒ (x, x) ∈ R  equivalence

B. R = {(L₁, L₂) : L₁ ⊥ L₂  for  L₁, L₂ ∈ L

so (L₁, L₁) ∉ R as on line is perpendicular to itself

(L₁, L₂) ∈ R  ⇒  (L₂, L₁) ∈ R  (symmetric)         →    I

(L₁, L₂) ∈ R ,  (L₂, L₃) ∈ R

⇒ (L₁, L₃) ∉ R  as  L₁ ⊥ L₂   L₂ ⊥ L₃

⇒ L₁ || L₂

C. y = 2 - 3x → linear function

so  $\frac{2-y}{3} = x$ ⇒ for every y ∈ R        →     III

there event atleast one x

y₁ = y₂  ⇒  2 - 3x₁ = 2 - 3x₂

⇒ x₁ = x₂ ⇒ bijective

D. f : [0, 1] → R

y = 1 + x² 

so  $x = \sqrt{1-y}$

⇒ one, one        →    II

for y = 5 not defined but for every y, x is unique as x ∈ [0, 1]