Is it possible to prove this set inequality given the constraints?

In summary, it is possible to prove a set inequality without using calculus by utilizing other mathematical techniques such as algebra, geometry, and logic. The common constraints when proving a set inequality include the values or variables in the set, the operations involved, and any given additional information or conditions. However, not all set inequalities can be proven due to their complexity or lack of information. Mathematical software programs can also be used to prove set inequalities, but it is important to have a thorough understanding of the logic and techniques behind the proof. To ensure the correctness of a proof, it must follow the rules of mathematical logic and be supported by evidence and reasoning, and it is recommended to have someone else review it for any errors or oversights.
  • #1
ainster31
158
1

Homework Statement



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Homework Equations



I have to use these set identities:

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The Attempt at a Solution



Pretty sure this is impossible since it's an inequality.
 
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  • #2
ainster31 said:
Pretty sure this is impossible since it's an inequality.
I thunk you can convert the inequality in two equalities with the right set and theorem 6.2.3.
 
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  • #3
mfb said:
I thunk you can convert the inequality in two equalities with the right set and theorem 6.2.3.

Nice, I proved it using this and it only took 19 steps.
 
Last edited:

Related to Is it possible to prove this set inequality given the constraints?

1. Can a set inequality be proven without using calculus?

Yes, it is possible to prove a set inequality using other mathematical techniques such as algebra, geometry, and logic.

2. What are the common constraints when trying to prove a set inequality?

The most common constraints when trying to prove a set inequality include the given values or variables in the set, the operations involved, and any additional information or conditions given.

3. Is it always possible to prove a set inequality?

No, there are some inequalities that cannot be proven due to their complexity or lack of information. In some cases, it may also depend on the specific constraints of the problem.

4. Can a computer program be used to prove a set inequality?

Yes, there are mathematical software programs that can be used to prove set inequalities. However, it is important to understand the logic and techniques behind the proof in order to validate the results.

5. How can I know if my proof of a set inequality is correct?

A proof of a set inequality is considered correct if it follows the rules of mathematical logic and is supported by evidence and reasoning. It is also helpful to have someone else review your proof for any errors or oversights.

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