What are the formulas for solving sets A and B?

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Discussion Overview

The discussion revolves around the mathematical formulas related to set theory and probability, specifically focusing on how to express various conditions involving two sets, A and B. The context includes preparation for a final exam, with participants seeking clarification on the appropriate symbolic representations for different scenarios involving these sets.

Discussion Character

  • Homework-related
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant requests specific formulas to solve for conditions involving sets A and B, including scenarios for neither set, either set, and conditional situations.
  • Another participant suggests using symbolic representations such as $A \cap B$ and $A^c$ to denote the sets and their complements.
  • Several participants discuss the application of probability rules, including the Special Addition Rule and Conditional Probability, in relation to the questions posed.
  • One participant expresses frustration over needing to memorize formulas without understanding the underlying concepts, emphasizing a desire for straightforward answers for exam preparation.
  • Another participant encourages the learner to articulate their understanding rather than simply seeking answers, prompting them to think about the symbolic language for "A or B" and "A and B."

Areas of Agreement / Disagreement

Participants do not reach a consensus on how to best approach the problems, with some focusing on the need for specific formulas while others emphasize understanding the concepts behind the formulas.

Contextual Notes

There are indications of missing assumptions regarding the learner's familiarity with set theory and probability concepts, as well as the specific requirements of the exam questions. The discussion reflects a range of understanding among participants.

nickar1172
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Which formula's would you use to solve each set and please show the actual formulas please thank you for the help I really appreciate it as I need to know this for my final exam tomorrow, thank you!

a) solving for neither set A and neither set B b) Solving for set A or Set B, but not bothc) Solving for set B given set Ad) Solving for set B given that he does not have Set A
 
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Hi again,

I probably need some more information. Are you simply asked to write these concepts mathematically, like $A \cap B$?
 
Jameson said:
Hi again,

I probably need some more information. Are you simply asked to write these concepts mathematically, like $A \cap B$?

Yes that is exactly what I am talking about
 
nickar1172 said:
Yes that is exactly what I am talking about

Ok well we can use $A, A^c, B, B^c$ for referring to the sets and we can also use $\cup, \cap$. What do you get for the first one?

(by the way, $\cup$ means "or" and $\cap$ means "and")
 
If I new I wouldn't be asking the question...
Postulates for Probability - P(A) >= 0, P(S) = 1
Special Addition Rule (mutually exclusive) - If A ∩ B = ∅, then P(A ∪ B) = P(A) + P(B)
General Addition Rule - P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
Probability and Odds (odds of A to B) - a / (a + b)
Conditional Probability - P(A | B) = P(A ∩ B) / P(B) provided that P(B) ≠ 0
General Multiplication Rule - P(A ∩ B) = P(A) . P(B | A)
Special Multiplication Rule(Independent events) - P(A ∩ B) = P(A) . P(B)
Multiplication Rules - if event B is independent of event A, then P(B | A) = P(A)

according to any of these rules how do you answer those question because I have NO IDEA how to
 
I didn't ask you what the correct answer was, rather what you think it is. If I just give you the answer that isn't helping you very much. We try to help you learn the material so you can answer it yourself. :)

Ok, (a) is $A^c \cap B^c$. Put into words this is "not A and not B". For (b), what is "A or B" in symbolic language? What is "A and B"?
 
I know what and or means I just need to know how to solve those questions, at this point it is not about "understanding" anything I just need to put this down on a formula sheet these answers so when I see this on the exam I know what to plug in like a machine, the entire semester has passed and I still don't know and I don't want to understand I just want to get an 80 on my test tomorrow so I don't fail the class all I need is those answered in mathematical notation if you can help me than I greatly appreciate it if not than no problem
 

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