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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 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.


Grade:12th Pass

1 Answers

santhanagopalan raghavan
33 Points
9 years ago

since the function is invertible(one to one and onto) only in D. The answer is (c)

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