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# If X and Y are two non-empty sets where f:X-> Y is function defined such that f(c)={f(x):xεC} for C SUBSET OF Xand f-1(D)={x: f(x)εD} for D SUBSET OF Y, for any A subset of Y and B subset of 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 is subset of f(x)(d) f{f-1(B)}=BExplain

Jitender Singh IIT Delhi
6 years ago
Ans:
X & Y are both non-empty set.
$f:X\rightarrow Y$
$f^{-1}(D) = x, f(x)\epsilon D$
D is any subset of Y. So all the f(x) elements belong to D are invertible.
$f^{-1}(f(x)) = x$
So, B is a subset of f(x), then it is invertible.
$f(f^{-1}(B)) = B$
Thanks & Regards
Jitender Singh
IIT Delhi