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

AI Thread Summary
The discussion revolves around proving that if A is a subset of C and B is a subset of D, with A intersecting B being empty (A∩B=Ø), then C intersecting D must also be empty (C∩D=Ø). A participant mistakenly identified the problem as biconditional, prompting clarification that it is not. The thread was redirected to the homework section for appropriate assistance. The conversation emphasizes the need for clear understanding in set theory proofs. The topic highlights the importance of proper categorization in forum discussions.
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.
 

Thread 'Formal derivation of statement from Peano Arithmetic system'

I was reading a Bachelor thesis on Peano Arithmetic (PA). PA has the following axioms (not including the induction schema): $$\begin{align} & (A1) ~~~~ \forall x \neg (x + 1 = 0) \nonumber \\ & (A2) ~~~~ \forall xy (x + 1 =y + 1 \to x = y) \nonumber \\ & (A3) ~~~~ \forall x (x + 0 = x) \nonumber \\ & (A4) ~~~~ \forall xy (x + (y +1) = (x + y ) + 1) \nonumber \\ & (A5) ~~~~ \forall x (x \cdot 0 = 0) \nonumber \\ & (A6) ~~~~ \forall xy (x \cdot (y + 1) = (x \cdot y) + x) \nonumber...
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