Relations and Functions: Class 12

04/08/2020 0 0

Relation:  A relation, R, from a non-empty set A to another non-empty set B, is mathematically defined as an arbitrary subset of the cartesian product of A and B. 

Domain, Range and Co-domain of the Relation 

Types of relations: 

  1. Empty relation   
  2. Universal relation: 
  3. Identity relation 
  4. Reflexive relation
  5. Symmetric relation 
  6. Transitive relation
  7. Equivalence relation
  8.  Inverse relation

Types of Intervals:

  • open interval 
  • second closed interval  
  • open closed interval
  • closed open interval

Function: Function is a relation for which each value from set the first component of the ordered pair is associated with exactly one value from the set of second components of the ordered pair.

Important functions

  • identity function
  • modulus function or absolute value functions
  • greatest integer function or integral function or step function
  • smallest integer function
  • Signum function
  • exponential functions
  • logarithmic function

 type of functions

  • One-One function Or injective function Or injection fashion
  • Onto function or subjective functions or surjection function
  • One-one onto function or bijective function Or bijection functions
  • identity function
  • Equal function
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