Class XII

A function f : X → Y is defined to be one – one (or injective), if --------------------------------------------------------------------------------
  1. the images of distinct elements of X under f are identical
  2. the images of distinct elements of X under f are not distinct
  3. the images of distinct elements of X under f are not defined
  4. the images of distinct elements of X under f are distinct
The range of function f(x) = [x] is :
  1. -------------------------------------------------------------------------------- Q (set of rational No.)
  2. R – Z
  3. Z
  4. R
A relation R on a non – empty set A is an equivalence relation iff it is
  1. symmetric and transitive
  2. reflexive, symmetric and transitive
  3. Reflexive ,antisymmetric,transitive
  4. reflexive
If A = { 1, 2, 3}, then the relation R = {(1, 2), (2, 3), (1, 3)} in A is
  1. -------------------------------------------------------------------------------- symmetric and transitive only
  2. symmetric only
  3. transitive only
  4. reflexive only
Let A = {a, b, c} and R = {(a, a), (b, b), (c, c), (b, c) } be a relation on A. Here, R is
  1. Transitive
  2. anti – symmetric
  3. symmetric
  4. reflexive
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