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

Given, S $= \{a, b, c \}$ and T $= \{1, 2, 3\}$
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(i) F $= \{(a, 3), (6, 2), (c, 1)\}$

i.e. F(a) $=$ 3, F(b) $=$ 2, F(c) $=$ 1

$\Rightarrow$ ${F^{ - 1}}$(3) $=$ a, ${F^{ - 1}}$(2 ) $=$ b, ${F^{ - 1}}(1)$ $=$c

$\therefore$ ${F^{ - 1}} = \{(3, a), (2, b), (1, c)\}$

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

F is not one-one function, since element b and c have the same image 1, so ${F^{ - 1}}$ does not exist.