Question:
Let A = {1, 2, 3}. Write all one-one from A to itself.
Solution:
A ={1, 2, 3}
Number of elements in A = 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 )}