Functions
- Details
- Category: Algebra
A function is a relationship between two sets. Unlike any general relationship,the function is a special relationship satisfying the following two criteria
A) Every element from the first set bears the relationship with oem element from the second set
B) No element from the first set bears the relationship with more than one element from the second set
Here are some examples:
Consider Sets A = {a,b,c,d) and B = {1,2,3}
Relation F1 : A ---> B = {(a,1), (b,2), (c,3)} is not a function since element d from set A does not relate to any elemtn from set B
Relation F2 : B ---> A = {(1,d), (2,c), (3,a)} is a function since each element of B relates to exactly one element of A
Relation F3 : B ---> A = {(1,b), (2,b), (3,b)} is also a function since each element of B relates to exactly one element of A
Relation F1 : A ---> B = {(a,1), (a,2), (b.3), (c,3), (d,1)} is not a function since element a from set A relates to two elements 1 and 2 from set B.