Proving Subset Inclusion for Intersection of Function Images

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Homework Help Overview

The discussion revolves around proving subset inclusion related to the intersection of function images, specifically focusing on the properties of functions and their images under union and intersection of subsets.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the validity of the second statement regarding subset inclusion, with some expressing doubt about its truth. There are attempts to clarify the proof structure and the reasoning behind it, including references to element proofs.

Discussion Status

The discussion is ongoing, with some participants questioning the completeness of the proof provided and seeking clarification on the reasoning. There is no explicit consensus on the validity of the second statement, and multiple interpretations are being explored.

Contextual Notes

Participants are navigating the requirements of the homework problem, with one expressing uncertainty about the initial setup and another correcting a previous statement. There is an emphasis on the need for a complete proof.

Bipolarity
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Homework Statement



Suppose f: A → B and that E,F are subsets of A.
Prove the following:
a) [itex]f(E \cup F) \equiv f(E) \cup f(F)[/itex]
b) [itex]f(E \cap F) \subset f(E)\cap f(F)[/itex]

Homework Equations



The Attempt at a Solution


So far I have solved the first one, but I am having trouble with the second. I have no idea where to begin.

BiP
 
Last edited:
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I don't believe b) is true..
 
Woops! Sorry I wrote it wrong. I'll change that.

BiP
 
Ok you that should just be a straight element proof then, just follow your nose, if b is in f(E∩F) then there exists an a in E∩F such f(a)=b, if a is in E∩F then a is in E and F.. and so on and so forth.
 
What does "and so on and so forth" supposed to mean? I don't understand your proof sorry. It's incomplete.

BiP
 
Bipolarity said:
It's incomplete.

Yes, because you are supposed to finish it.
 

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