RELATION AND FUNCTION - L1

Let R be a relation on the set of all line in a plane defined by (l_(1),l_(2))in R hArr l in el_(1) is parallel to line l_(2). Show that R is an equivalence relation.

Let A be the set of all lines in xy-plane and let R be relation in A , defind by R={(L_(1),L_(2)):L_(1)||L_(2)}. show that R is an equivalence relation in A. Find the set of all lines related to the line Y=3x+5.

Students of Grade 9, planned to plant saplings along straight lines, parallel to each other to one side of the playground ensuring that they had enough play area. Let us assume that they planted one of the rows of the saplings along the line y=x-4 . Let L be the set of all lines which are parallel on the ground and R be a relation on L. Answer the following using the above information. Let relation R be defined by R={L1,L2):L1||L2 where L_(1),L_(2) in L} then R is ______ relation

Consider the relation 4l^(2)-5m^(2)+6l+1=0 , where l, m inR . The line lx+my+1=0 touches a fixed circle whose equation is

Let R be the relation over the set of all straight lines in a plane such that l_1\ R\ l_2hArrl_1_|_l_2 . Then, R is (a) symmetric (b) reflexive (c) transitive (d) an equivalence relation

Let L be the set of all lines in XY= plane and R be the relation in L defined as R={(L_(1),L_(2)):L_(1) is parallel to L_(-)2} Show that R is an equivalence relation.Find the set of all lines related to the line y=2x+4.

Let L be the set of all lines in XY -plane and R be the relation in L defined as R={(L_(1),L_(2)):L_(1) is parallel to L_(2)}. Show that R is an equivalence relation.Find the set of all lines related to the line y=2x+4

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.

Relation And Functions

Let L be the set of all lines in the plane and R be the relation in L, defined as : R = { (l_(i),l_(j))=l_(i) is parallel to l_(j),AA i,j }. Show that R is an equivalence relation. Find the set of all lines related to the line y=7x+5 .