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.

L.et A be the set of all 50 students of class X in a school. Let f : A → N be function defined by f (x) = roll number of student x. Show that f is one-one but not onto.

 Check the injectivity and surjectivity of the following functions :

(i) f : N → N given by f (x) = x²
(ii)    f : Z → Z given by f (x) = x²
(iii)    f : R → R given by f (x) = x² (iv) f : N → N given by f (x) = x³
(v) f : Z → Z given by f (x) = x³

250. Show that the modulus function f : R → R, given by f (x) = | x |, is neither one-one nor onto, where |x| is x, if x is positive or 0 and | x | is —x, if. x negative.