Mathematics - Online Test

Consider any a ,b , c ∈$\in$A .

1. Since both a and a must be either even or odd, so (a , a) ∈R ⇒R is reflexive.
2. Let (a ,b) ∈R ⇒ both a and b must be either even or odd, ⇒ both b and a must be either even or odd, ⇒ ( b ,a) ∈R .Thus , (a ,b) ∈R ⇒ ( b ,a) ∈R ⇒R is symmetric.
3. Let (a ,b) ∈R and (b ,c) ∈R ⇒ both a and b must be either even or odd, also ,both b and c must be either even or odd, ⇒ all elements a, b and c must be either even or odd, ⇒ ( a ,c) ∈R . Thus , (a ,b) ∈R ⇒ ( b ,c) ∈R ⇒ (a ,c) ∈R ⇒R is transitive.

The equation of the pair of straight lines paasing through the origin is fiven by is given by ax2 + 2hxy + by2 =0

The condition for perpendicularity between the pair of lines is a+b = 0

Hence the locus of the pair of these perpendicular straight lines should be xy = 0

p∨∼p≡T

T∨p≡T