Let S = {a,b,c} and T= {1,2,3}.
Find \(F^{-1}\) of the following functions F from S to T, if it exists.
I. F={(a,3),(b,2),(c,1)}
II. F={(a,2),(b,1),(c,1)}
Let S = {a,b,c} and T= {1,2,3}.
Find \(F^{-1}\) of the following functions F from S to T, if it exists.
I. F={(a,3),(b,2),(c,1)}
II. F={(a,2),(b,1),(c,1)}
Solution and Explanation
S = {a, b, c}, T = {1, 2, 3}
(i) F: S \(\to\) T is defined as:
F = {(a, 3), (b, 2), (c, 1)}
\(\Rightarrow\) F (a) = 3, F (b) = 2, F(c) = 1
Therefore, F−1: T \(\to\) S is given by
\(F^{-1}\) = {(3, a), (2, b), (1, c)}.
(ii) F: S \(\to\) T is defined as:
F = {(a, 2), (b, 1), (c, 1)}
Since F (b) = F (c) = 1,
F is not one-one.
Hence, F is not invertible i.e., \(F^{-1}\) does not exist.
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