How do you construct proofs for set unions?

In summary, the conversation is about proving the statement (∃y)(∀x)(x ∈ y) ↔ (x ∈ a ∨ x ∈ b)) and the use of the union axiom in ZF to derive it. The individual asking for help is unsure of how to construct proofs and is seeking clarification and further information. The conversation also touches on the importance of understanding the basics of set theory and the potential consequences of relying on others to do the work for you.
  • #1
fruitjunkie
5
0
union proof due at midnight!

(∃y)(∀x)(x ∈ y) ↔ (x ∈ a ∨ x ∈ b))
How do you prove this??
 
Physics news on Phys.org
  • #2


In ZF, that is an axiom. But I think you don't really mean that. So could you elaborate??
 
  • #3


it is a lemma that my professor asked us to prove.
 
  • #4


So, what did you try already??
 
  • #5


i actually don't know how to construct proofs..
 
  • #6


i don't get it. the letters a and b seem to be unbound variables, hence meaningless. so there is no statement here. what gives??
 
  • #7


oops, i forgot the beginning: Given sets a and b, there is a set containing exactly the elements from a and b:
 
  • #8


It's well past midnight but that is just as well. If you honestly do not "how to construct proofs" your professor needs to know that so he/she can teach you. If you get someone else to do the problem for you, the professor might think you already know how and not discover the mistake until an exam!

In any case, I doubt that anyone here could give a proof that you would understand without knowing what basics info you have about sets. As micromass said, in ZF, that's an axiom. What "axioms" or operations do you have to work with?
 
  • #9


HallsofIvy said:
It's well past midnight but that is just as well. If you honestly do not "how to construct proofs" your professor needs to know that so he/she can teach you. If you get someone else to do the problem for you, the professor might think you already know how and not discover the mistake until an exam!

In any case, I doubt that anyone here could give a proof that you would understand without knowing what basics info you have about sets. As micromass said, in ZF, that's an axiom. What "axioms" or operations do you have to work with?

The "union axiom" can be derived from the sum axiom and the pairing axiom, as well the proper definitions attached to both of these.
 

1. What is "union proof due at midnight"?

"Union proof due at midnight" refers to a deadline set by a company or organization for employees to submit any necessary documentation or information related to unionization efforts. This could include voting on union representation, signing authorization cards, or providing personal information.

2. Why is there a deadline for "union proof due at midnight"?

The deadline for "union proof due at midnight" is typically set by the company to ensure that all necessary information is gathered in a timely manner. It also allows for any potential challenges or disputes to be addressed before a final decision is made.

3. What happens if I miss the deadline for "union proof due at midnight"?

If an employee misses the deadline for "union proof due at midnight", they may not be able to participate in any unionization efforts or have their voice heard in the decision-making process. It is important to adhere to the deadline set by the company to ensure that your rights as an employee are protected.

4. Is "union proof due at midnight" a common practice?

Yes, setting a deadline for "union proof due at midnight" is a common practice in companies and organizations where employees are considering unionization. This allows for an organized and efficient process for both the company and the employees.

5. Can the deadline for "union proof due at midnight" be extended?

In some cases, the deadline for "union proof due at midnight" can be extended if there are extenuating circumstances. However, it is important to communicate with the company or union organizers if you are unable to meet the deadline to avoid any potential issues or disputes.

Similar threads

  • Precalculus Mathematics Homework Help
Replies
3
Views
818
  • Precalculus Mathematics Homework Help
Replies
11
Views
1K
  • Precalculus Mathematics Homework Help
Replies
1
Views
1K
  • Set Theory, Logic, Probability, Statistics
Replies
1
Views
760
  • Calculus and Beyond Homework Help
Replies
12
Views
1K
  • Precalculus Mathematics Homework Help
Replies
18
Views
1K
  • Precalculus Mathematics Homework Help
Replies
10
Views
2K
  • Set Theory, Logic, Probability, Statistics
Replies
4
Views
2K
  • Topology and Analysis
Replies
2
Views
1K
  • Precalculus Mathematics Homework Help
Replies
5
Views
1K
Back
Top