Let L be the set of all lines in a plane and R be the relation in L defined as `R = {(L _(1), L _(2)) : L _(1)` is perpendicular to `L _(2)` }. Show that R is symmetric but neither reflexive nor transitive.

On a set of natural numbers let R be the relation defined by aRb if a + 2b = 15. Write down the relation by listing all the pairs. Check whether it is reflexive, symmetric, transitive, equivalence.

Let R be the relation over the set of all straight lines in a plane such that l_(1) Rl_(2) hArr l_(1)bot l_(2) . Then R is

If line l_1 is perpendicular to line l_2 and line l_3 has slope 3 then find the equation of line l_1

If line l_1 is perpendicular to line l_2 and line l_3 has slope 3 then find the equation of line l_2

Show that the relation R in the set {1,2,3} given by R = {(1,1) ,(2,2),(3,3) , (1,2), (2,3)} is reflexive but neither symmetric nor transitive.

On the set of natural number let R be the relation defined by aRb if 2a +3b=30. Write down the relation by listing all the pair . check whether it is (i) reflexive (ii) symmetric (iii) transitive (iv) equivalence

Show that the relation R in the set R of real numbers, defined as R={(a ,b): alt=b^2} is neither reflexive nor symmetric nor transitive.