Question

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)}

Answer 1

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)}.

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(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.