Question
If A = {1, 2, 3}, show that a one-one function f : A → A must be onto.
✓
Answer
A = {1, 2, 3}
Number of elements in A = 3
Number of one-one functions = number of ways of arranging 3 elements = 3! = 6
So, the possible one-one functions can be the following:
So, all the functions are onto.
Number of elements in A = 3
Number of one-one functions = number of ways of arranging 3 elements = 3! = 6
So, the possible one-one functions can be the following:
- {(1, 1), (2, 2), (3, 3)}
- {(1, 1), (2, 3), (3, 2)}
- {(1, 2 ), (2, 2), (3, 3)}
- {(1, 2), (2, 1), (3, 3)}
- {(1, 3), (2, 2), (3, 1)}
- {(1, 3), (2, 1), (3, 2)}
So, all the functions are onto.
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