Teration 8 Show that the relation R in the set A 1 2 3 4 5 given by R a b ab is even is an equivalence relation Show that all the elements of 1 3 5 are related to each other and all the elements of 2 4 are related to each other But no element of 1 3 5 is related to any element of 2 4 9 Show that each of the relation R in the set A x 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 relate 10 Give an example of a relation Which is elle 1 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 transitive but not reflexive 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 an equivalence relation Further show that the set of all points related to a point P 0 0 is the circle passing through P with origin as centre 12 Show that the relation R defined in the set A of all triangles as R T T T is similar to T is equivalence relation Consider three right angle triangles T with sides 3 4 5 T with sides 5 12 13 and T with sides 6 8 10 Which triangles among T T and T are related ollec 13 Show that the relation R defined in the set A of all polygons as R P P P and P have same number of sides is an equivalence relation What is the set of all elements in A related to the right angle triangle T with sides 3 4 and 5 1 in each case 14 Let L be the set of all lines in XY plane and R be the relation in L defined as R L L L is parallel to L Show that R is an equivalence relation Find the set of all lines related to the line y 2x 4 Rationalised 2023 24 11 RELATIONS AND FUNCTIONS 7 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 symmetric C R is symmetric and transitive but not reflexive D R is an equivalence relation 16 Let R be the relation in the set Ngiven by R a b a b 2 b 6 Choose the correct answer A 2 4 ER B 3 8 R C 6 8 R D 8 7 R 1 3 Types of Functions The notion of a function along with some special functions like identity function constant function polynomial function rational function modulus function signum function etc along with their graphs have been given in Class XI