If X and Y are two non- empty sets where \[f:X\to Y\]is function is defined such that \[f(c)=\left\{ f(x):x\in C \right\}\]for \[C\subseteq X\]and \[{{f}^{-1}}(D)=\{x:f(x)\in D\}\]for \[D\subseteq Y\] for any \[A\subseteq X\] and \[B\subseteq Y,\]then [IIT Screening 2005]

\[{{f}^{-1}}(f(A))=A\]only if \[f(x)=Y\]

\[f({{f}^{-1}}(B))=B\] only if \[B\subseteq f(X)\]

If X and Y are two non- empty sets where \[f:X\to Y\]is function is

1.	If X and Y are two non- empty sets where \[f:X\to Y\]is function is defined such that \[f(c)=\left\{ f(x):x\in C \right\}\]for \[C\subseteq X\]and \[{{f}^{-1}}(D)=\{x:f(x)\in D\}\]for \[D\subseteq Y\] for any \[A\subseteq X\] and \[B\subseteq Y,\]then [IIT Screening 2005]
A.	\[{{f}^{-1}}(f(A))=A\]
B.	\[{{f}^{-1}}(f(A))=A\]only if \[f(x)=Y\]
C.	\[f({{f}^{-1}}(B))=B\] only if \[B\subseteq f(X)\]
D.	\[f({{f}^{-1}}(B))=B\]
Answer» D. \[f({{f}^{-1}}(B))=B\]

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If X and Y are two non- empty sets where \[f:X\to Y\]is function is defined such that \[f(c)=\left\{ f(x):x\in C \right\}\]for \[C\subseteq X\]and \[{{f}^{-1}}(D)=\{x:f(x)\in D\}\]for \[D\subseteq Y\] for any \[A\subseteq X\] and \[B\subseteq Y,\]then [IIT Screening 2005]

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