Set Theory Proof Help: Proving C∩D=Ø When A⊆C and B⊆D

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Discussion Overview

The discussion revolves around a set theory proof involving the relationships between sets A, B, C, and D, specifically addressing the claim that if A is a subset of C and B is a subset of D, and A and B are disjoint, then C and D must also be disjoint. The scope includes aspects of proof methodology and clarification of logical statements.

Discussion Character

  • Homework-related

Main Points Raised

  • One participant seeks assistance with a proof regarding the relationship between sets, specifically questioning whether they need to prove a biconditional statement.
  • Another participant questions the classification of the statement as a biconditional and requests clarification on the user's progress with the problem.
  • A subsequent post acknowledges the misunderstanding regarding the biconditional nature of the statement.

Areas of Agreement / Disagreement

Participants do not reach a consensus, as there is a misunderstanding about the nature of the statement being discussed, and the thread is closed before further exploration occurs.

Contextual Notes

The initial claim's biconditional nature is not clearly established, leading to confusion about the proof requirements.

dainty77
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Hey guys!

I am new to this forum but saw the helpful posts on set theory proofs and wondered if I could finally get some help with this problem:

Suppose A, B, C, and D are sets with A⊆C and B⊆D. If A∩B=Ø then C∩D=Ø.

This is a biconditional so I have to prove it both ways correct?

Any help would be greatly appreciated!
 
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This belongs in the homework forum. Do you have some attempt?

I don't see a biconditional in your statement.
 
Oh my mistake!
 
Thread closed as dainty77 posted this question (per R136a1's suggestion) in the homework section.
 

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