ONTO ONE TO ONE FUNCTION.ppt
- 1. BS SE(1B)EVENING COURSE:DISCRETE STRUCTURE UIIT GROUP NO:8 GROUP MEMBERS: 1.SAJAL ASGHAR 2.M.MUAWWAZ USMAN 3.M.SAAD MALIK UIIT(UNIVERSITY INSTITUTE OF INFORMATION TECHNOLOGY)
- 2. OUTLINE OF TODAY’S PRESENTTATION: ONE-ONE FUNCTION. ONTO FUNCTION BIJECTIVE FUNCTION.
- 3. ONE-ONE FUNCTION(INJECTIVE) DEFINATION:- “A function of from set ‘A’ to set ‘B’ is one-one Function if no two elements in ‘A’ are mapped To same element in ‘B’ ” Distinct elements form distinct images. We cannot mapped with same elements. Value of ‘x’ elements must be equal to ’y’. Value of ‘y’ must be greater than ‘x’.
- 5. |A|<|B| How many one to one functions are possible? Total number of element in set ‘A’ is |x|. Total number of elements in set ‘B’ is |Y|. I have ‘y’ number of choices for first element of set ‘A’. {y(y-1) (y-2) (y-3)…….y-(x-1)} So we can derive formula from this series. yPx =4P3 this is how to write formula 1 2 3 A C B k
- 6. ONTO FUNCTION (surjection) DEFINATION:- ‘A function ‘f’ from set ‘A’ to set ‘B’ is onto if each element of ’B’ is mapped to at least one element of ‘A’. Range of f=B. In onto function range equals to the elements of set B. If both range and co-domains are equal so it is onto function. |A|>|B| A B C 1 2 3 1 2 3 A B
- 7. If one-one then onto? If onto then one-one? How many onto functions if |A|=|B|? 1 2 3 A B 1 2 3 A B C d 1 2 3 A B c
- 8. BIJECTIVE FUNCTION: DEFINATION:- “A Function f : A&B bijection if ‘f’ is both one-one & onto.” One-one function:- ( |A| < |B| ) Onto function:- ( |A| > |B| ) If you want to make bijective function then number of element of set ‘A’ must be equal to the elements of set of set ‘B’. |A|=|B|
- 9. EXAMPLES:- 1. First is one-one but not onto. 2. Second is onto but not one-one. 3. Third is one-one & onto. 1 2 3 4 A B c 1 2 3 A B C d 1 2 3 A B c