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

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1.Relation and Function

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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

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

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

(IIT-2005)

Solution

(c) The set $B$ satisfied the above definition of function $f$

so option $(c)$ is correct.

Standard 12

Mathematics

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