Question

let L be the set of straight lines on the rectangular Cartesian plane . If we define a relation R on L as 'x is perpendicular to y for x,y belongs to L" then state whether or not R is (I) reflective (ii) symmetric (iii) transitive (iv) anti- symmetric

*refer to ncert 10 adv maths ex.no. 1.4 no. 11*​

Answer 1

$\huge\bold{\textbf{\textsf{{\color{cyan}{Answer}}}}}$

Let L be the set of all lines in a plane and R be the relation in L defined as R = {(L1, L2): L₁ is perpendicular to L2). Show that R is symmetric but neither reflexive nor transitive.

R= ((L1, L2): L₁ is perpendicular to L2 Since no line can be perpendicular to itself.. R is not reflexive.

Let (L₁, L₂) ER

.. L₁ is perpendicular to L2 L2 is peipendicular to L₁

→ (L2, L₁) ER

(L₁L2) ER⇒ (L2, L₁) ER

.. R is symmetric

Again we know that if L₁ is perpendicular to L2 and L2 is perpendicular to L3, then L₁can never be perpendicular to

L3.

(L1, L2) ER, (L2, L3) ER does not imply (L1, L3) ER

.. R is not transitive.