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Question
If A = {1, 2, 3, 4} and B = {a, b, c, d}, define any four bijections from A to B. Also give their inverse functions.
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Solution
f1={ (1, a), (2, b), (3, c), (4, d)} ⇒ f1−1 ={(a, 1), (b, 2), (c, 3), (d, 4)}
f2={(1, b), (2, a), (3, c), (4, d)} ⇒f2−1 {(b, 1), (a, 2), (c, 3), (d, 4)}
f3= { (1, a), (2, b), (4, c), (3, d)} ⇒ f3−1 {(a, 1), (b, 2), (c, 4), (d, 3)}
f4 = {(1, b), (2, a), (4, c), (3, d)} ⇒ f4−1 = {(b, 1), (a, 2), (c, 4), (d, 3)}
Clearly, all these are bijections because they are one-one and onto.
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