How Do You Solve Complex Venn Diagram Problems Involving Sets?

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Discussion Overview

The discussion revolves around solving complex Venn diagram problems involving set operations. Participants are tasked with finding specific sets based on given universal and subset definitions, focusing on operations such as intersection and union.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant requests help with set operations involving the universal set of lowercase English letters, vowels, and letters from the words "spring" and "garden".
  • Another participant questions whether the operation intended was the intersection of sets G and V, seeking clarification on the meaning of the intersection symbol (∩).
  • A later reply confirms that ∩ denotes intersection and explains that G' represents elements of the universal set not in G, prompting further exploration of the specific sets requested.
  • Participants are encouraged to identify the elements of the sets based on the operations outlined, such as finding the intersection of G' and V, and the union of G, V, and S.

Areas of Agreement / Disagreement

There is no consensus on the solutions to the set operations, as participants are still exploring the definitions and implications of the operations involved.

Contextual Notes

Participants have not fully resolved the specific elements of the sets or the outcomes of the operations, indicating potential gaps in understanding or assumptions about set definitions.

dizzieko03
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Can someone please break down how to do this one? I'm absolutely stumped on this one. Thank you very much. :)Use the following sets to complete the operations.
Universal set = {lower case English letters; a,b,c,d…x,y,z}
V = {a,e,i,o,u}
S = {letters in the word “spring”}
G = {letters in the word “garden”}

Find the following sets:

a. G’ ∩ V
b. (G ∩ V) ∩ { }
c. (G ∪ V ∪ S)
 
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dizzieko03 said:
Can someone please break down how to do this one? I'm absolutely stumped on this one. Thank you very much. :)Use the following sets to complete the operations.
Universal set = {lower case English letters; a,b,c,d…x,y,z}
V = {a,e,i,o,u}
S = {letters in the word “spring”}
G = {letters in the word “garden”}

Find the following sets:

a. G’ ∩ V
b. (G ∩ V) ∩ { }
c. (G ∪ V ∪ S)
Hello dizzieko03,
Welcome to MHB!
Is that a meant to be G ∩ V? Can you also explain to me what ∩ means, so I know where you are stuck.

Regards,
 
Petrus said:
Hello dizzieko03,
Welcome to MHB!
Is that a meant to be G ∩ V? Can you also explain to me what ∩ means, so I know where you are stuck.

Regards,

It must mean intersection .
 
dizzieko03 said:
Can someone please break down how to do this one? I'm absolutely stumped on this one. Thank you very much. :)Use the following sets to complete the operations.
Universal set = {lower case English letters; a,b,c,d…x,y,z}
V = {a,e,i,o,u}
S = {letters in the word “spring”}
G = {letters in the word “garden”}

Find the following sets:

a. G’ ∩ V
b. (G ∩ V) ∩ { }
c. (G ∪ V ∪ S)

Hello and welcome to MHB, dizzieko03! :D

a. $G'$ means those elements of $U$ which are not in $G$. $\cap$ means the intersection, so you want the elements that are in both sets only. So we have the letters of the alphabet not in the word "garden" which are also vowels. Can you give this set?

b. Here we want the letters in the word "garden" which are also vowels, and then find the intersection with the null set. What is the intersection of any set with the null set?

c. Here we want the letters in the word "garden" and all the vowels and all the letters in the word "spring". Can you list this set?

Post your work and we will be glad to look it over.
 

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