Question

Prove that \(f: X \rightarrow Y\) is an injection if and only if the equation \(\bar f^{-1}(\bar f)(A)=A\) holds that for all \(A \in P(X)\). Use this to prove that \(f: X \rightarrow Y\) is an injection if and only if \(\bar f^{-1}: P(Y) \rightarrow X\) is a surjective.

Answer 1

P for the powersets... meaning that all A belongs to a Powerset X... hmm oh maybe I should the definition of the inverse on this one... ... the powerset y implies powerset x is a surjective meaning that's it's onto

Answer 2

@Euler271

Answer 3

so f: X -> Y is an injection then that equation holds... so it's a one to one function

Answer 4

@tomhue

Answer 5

what is this o_o

i can't help with this

Answer 6

proving a function... I don't know either. xX)(WE*#(@)

Answer 7

which class is this?

Answer 8

introduction to advanced mathematics...but the majority of the topics are discrete math

Answer 9

@zzr0ck3r