- #1

cbarker1

Gold Member

MHB

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- Homework Statement
- Let #f:X \to Y# be a function. Show that if #f^{-1}({y})# is a singleton for all #y \in Y#.

- Relevant Equations
- Definition of Preimage is #f^{-1}(B)={ x\in X: f(x) \in B}# where B is a subset of Y.

#f^{-1}({y})={x}#

Dear Everyone,

I have some trouble how to start the proof of this statement. I need to prove the preimage of the singleton under f is the subset of singleton of x and vice versus. My attempt is this:Given y.

So we know that definition of the preimage is when all #x# is in #X# , then #f(x) \in B#.I am lost after these facts.

Thank for any assistance,

Cbarker1

I have some trouble how to start the proof of this statement. I need to prove the preimage of the singleton under f is the subset of singleton of x and vice versus. My attempt is this:Given y.

So we know that definition of the preimage is when all #x# is in #X# , then #f(x) \in B#.I am lost after these facts.

Thank for any assistance,

Cbarker1