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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 rarr 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)}="B only if "B subseteq f(x)`

D

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

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