Need help correcting this proof

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In summary, The incorrect proof provided a contradiction for the claim "For any sets S,T,and W,if S∩T≠0 and T∩W≠0,then S∩W≠0". However, this claim is false, as shown by the counterexample S=[0,3], T=[1,5], W=[4,10]. Therefore, there is no way to correct the proof.
  • #1
ash25
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Homework Statement


PLEASE HELP!How would you correct this incorrect proof:
Suppose that S∩T≠0,T∩W≠0,and for a contradiction S∩W=0.From the first 2,we have some t∈S∩T,and similarly t∈T∩W.But then t∈S,t∈T,and t∈W.So t∈S∩W,giving a contradiction.
 
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  • #2
There is no way to correct this "proof", since what you're trying to show is false!

Take [tex]S=[0,3],~T=[1,5],~W=[4,10][/tex]. Then [tex]S\cap W=\emptyset[/tex]...
 
  • #3
Thank you, so the claim was true though, right? It was:
For any sets S,T,and W,if S∩T≠0 and T∩W≠0,then S∩W≠0
 
  • #4
No, I just gave you a counterexample...
 
  • #5
You are being so helpful thank you!
but you are saying that the claim is false?
 
  • #6
ash25 said:
but you are saying that the claim is false?

Yes!
 

1. What is the purpose of a proof?

A proof is used to demonstrate the validity of a mathematical statement or argument. It serves as a logical and rigorous way to show that a statement or argument is true.

2. How do you know if a proof is correct?

A proof is considered correct if it follows the rules of logic and is based on accepted axioms and definitions. It should also be clear and easy to follow, with each step being logically connected to the previous one.

3. What are some common mistakes to look out for when correcting a proof?

Some common mistakes in proofs include incorrect use of definitions or axioms, incorrect logical reasoning, and missing or incorrect steps. It is also important to check for any assumptions that are not explicitly stated and make sure they are justified.

4. How can I improve my proof-writing skills?

Practice is key to improving your proof-writing skills. It is also helpful to read and analyze well-written proofs to understand the structure and logic behind them. Additionally, seeking feedback from peers or mentors can also help you identify areas for improvement.

5. What should I do if I am stuck on a proof?

If you are stuck on a proof, it can be helpful to break it down into smaller, more manageable parts. You can also try approaching the problem from a different angle or seeking assistance from a colleague or instructor. Don't be afraid to ask for help or take a break and come back to it with a fresh perspective.

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