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 t o L_2}` . Show that R is symmetric but neither reflexive nor transitive.

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.

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 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 .

Let L be the set of all lines in a plane and let R be a relation defined on L by the rule (x,y)epsilonRtox is perpendicular to y . Then prove that R is a symmetric relation on L .

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.

Let N be the set of all natural numbers and let R be relation in N. Defined by R={(a,b):"a is a multiple of b"}. show that R is reflexive transitive but not symmetric .

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

Let S be the set of all real numbers and let R be a relation in s, defined by R={(a,b):aleb}. Show that R is reflexive and transitive but not symmetric .

Let N be the set of all natural niumbers and let R be a relation in N , defined by R={(a,b):a" is a factor of b"}. then , show that R is reflexive and transitive but not symmetric .