Let A = {1, 2, 3}. Write all one-one from A to itself.
Question:

Let A = {1, 2, 3}. Write all one-one from A to itself.

Solution:

A ={1, 2, 3}
Number of elements in  = 3

Number of one-one functions = number of ways of arranging 3 elements $=3 !=6$

(i) {(1, 1), (2, 2), (3, 3)}
(ii) {(1, 1), (2, 3), (3, 2)}
(iii) {(1, 2 ), (2, 2), (3, 3 )}
(iv) {(1, 2), (2, 1), (3, 3)}
(v) {(1, 3), (2, 2), (3, 1)}
(vi) {(1, 3), (2, 1), (3,2 )}

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