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 , and ? . 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 = x + . . Let R be the relation in the set { , , , } given by R = {( , ), ( , ), ( , ), ( , ), ( , ), ( , ), ( , )}.
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. . Let R be the relation in the set N given by R = {( a , b ) : a = b – , b > }. Choose the correct answer.
(A) ( , ) ∈ R (B) ( , ) ∈ R (C) ( , ) ∈ R (D) ( , ) ∈ R . 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. Addition, subtraction, multiplication and division of two functions have also been studied.
As the concept of function is of paramount importance in mathematics and among other disciplines as well, we would like to extend our study about function from where we finished earlier. In this section, we would like to study different types of functions. Consider the functions f , f , f and f given by the following diagrams. In Fig .