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) $F = {(a, 2), (b, 1), (c, 1)}$

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Solution

$S = {a, b, c} T = {1, 2, 3} F = {(a, 3), (b, 2), (c, 1)} F^{- 1} = {(3, a), (2, b), (1, c)} F = {(a, 2), (b, 1), (c, 1)}$
The function is not invertibe since it is not bijective.

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