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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 X and 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)}=B Explain

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 X


and 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)}=B


Explain

Grade:12th Pass

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
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
askIITians Faculty

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