Grade 12th PassDifferential Calculus
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 pls.
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 pls.
