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If X and Y are two non-empty sets where...

If `X and Y` are two non-empty sets where `f: X->Y`,is function is defined such that `f(c) = {f (x): x in C}` for `C sube X and f^-1 (D) = {x: f(x) in D}` for `D sube Y`,for any `A sube Y and B sube Y`, then

A

`f^(1){f(A)}=A`

B

`f^(1){f(A)}=A," only if "f(X)=Y`

C

`f{f^(-1)(B)}, " only if " B sube f(x)`

D

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

Text Solution

Verified by Experts

The correct Answer is:
C
Since, only (c) satisfy given definition
i.e. `f{f^(-1)(B)}=B`
Only,if `B sube f(x)`
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