If X and Y are two non- empty sets where $f:X o Y$is function is defined such that $f(c)=\left\{ f(x):x\in C ight\}$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

Question

If X and Y are two non- empty sets where $f:X	o Y$is function is defined such that $f(c)=\left\{ f(x):x\in C ight\}$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

Accepted Answer

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

Answer

${{f}^{-1}}(f(A))=A$

Answer

${{f}^{-1}}(f(A))=A$only if $f(x)=Y$

Answer

$f({{f}^{-1}}(B))=B$

fun-lim

Question: 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

fun-lim

Question: 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

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