Let S={a, b, c} and T={1,2,3} . Find F^{-1} of following functions F from S to T . if it exists.&nbs

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1.Relation and Function

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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. $F =\{( a , 3),\,( b , 2),\,( c , 1)\}$

Option A

Option B

Option C

Option D

Solution

$S =\{ a , b , c \}, \,\,T =\{1,2,3\}$

$F : S \rightarrow T$ is defined as $F =\{( a , 3),\,( b , 2),\,( c , 1)\}$

$\Rightarrow $ $F ( a )=3, \,F ( b )=2,\, F ( c )=1$

Therefore, $F^{ -1}: T \rightarrow $ $S$ is given by $ F ^{-1}=\{(3, a ),\,(2, b ),\,(1, c )\}$

Standard 12

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