28. If $X$ and $Y$ are two non-empty sets where $f : X - - > Y$ is function is defined such that $\mathrm { f } ( \mathrm { c } ) = \{ \mathrm { f } ( \mathrm { x } ) : \mathrm { x }$ ÎC $\}$ for C ÍX and $f ^ { - 1 } ( D ) = \{ x : f ( x )$ Î $D \}$ for $D$ Í $y$, for any A Í X and B Í Y then : (a) $f ^ { - 1 } ( f ( A ) ) = A$ (b) $f ^ { - 1 } ( f ( A ) ) = A$ only if $f ( X ) = Y$ (c) $f \left( f ^ { - 1 } ( B ) \right) = B$ only if B Í $f ( x )$ (d) $f \left( f ^ { - 1 } ( B ) \right) = B$
Suppose $X$ and $Y$ are two sets and $f : X \longrightarrow Y$ is a function. For a subset $A$ of $X$, define $f ( A )$ to be the subset $\{ f ( a ) : a \in A \}$ of $Y$. For a subset $B$ of $Y$, define $f ^ { - 1 } ( B )$ to be the subset $\{ x \in X : f ( x ) \in B \}$ of $X$. Then which of the following statements is true?
28. If $X$ and $Y$ are two non-empty sets where $f : X - - > Y$ is function is defined such that $\mathrm { f } ( \mathrm { c } ) = \{ \mathrm { f } ( \mathrm { x } ) : \mathrm { x }$ ÎC $\}$ for C ÍX\\
and $f ^ { - 1 } ( D ) = \{ x : f ( x )$ Î $D \}$ for $D$ Í $y$, for any A Í X and B Í Y then :\\
(a) $f ^ { - 1 } ( f ( A ) ) = A$\\
(b) $f ^ { - 1 } ( f ( A ) ) = A$ only if $f ( X ) = Y$\\
(c) $f \left( f ^ { - 1 } ( B ) \right) = B$ only if B Í $f ( x )$\\
(d) $f \left( f ^ { - 1 } ( B ) \right) = B$