Category Relations

16. Let R be the relation in the set N given by R={(a,b) : a=b–2, b>6}. Choose the correct answer. (A) (2,4) (in) R       (B) (3,8) (in) R  (C) (6,8) (in) R  (D) (8,7) (in) R Relations and Functions Exercise…

15. Let R be the relation in the set {1,2,3,4} given by R={(1,2), (2,2), (1,1), (4,4), (1,3), (3,3), (3,2)}. Choose the correct answer. (A) R is reflexive and symmetric but not transitive. (B) R is reflexive and transitive but not…

14. Let L be the set of all lines in XY plane and R be the relation in L defined as R={(L1,L2) : L1 is parallel to L2}. Show that R is an equivalence relation. Find the set of all…

13. Show that the relation R defined in the set A of all polygons as R={(P1,P2) : P1 and P2 have same number of sides}, is an equivalence relation. What is the set of all elements in A related to…

12. Show that the relation R defined in the set A of all triangles as R={(T1,T2) : T1 is similar to T2}, is equivalence relation. Consider three right angle triangles T1 with sides 3,4,5, T2 with sides 5,12,13 and T3…

11. Show that the relation R in the set A of points in a plane given by R={(P,Q) : distance of the point P from the origin is same as the distance of the point Q from the origin}, is…

10. Give an example of a relation. Which is: (i) Symmetric but neither reflexive nor transitive. (ii) Transitive but neither reflexive nor symmetric. (iii) Reflexive and symmetric but not transitive. (iv) Reflexive and transitive but not symmetric. (v) Symmetric and…

9. Show that each of the relation R in the set A={x(in)Z : 0≤x≤12}, given by (i) R={(a,b) : |a–b| is a multiple of 4} (ii) R={(a,b) : a=b}  is an equivalence relation. Find the set of all elements related…