MHB How Do You Solve Complex Venn Diagram Problems Involving Sets?

AI Thread Summary
The discussion revolves around solving complex Venn diagram problems involving set operations with specific sets defined by letters. The user is seeking help with three specific operations: finding the intersection of the complement of set G with set V, the intersection of sets G and V with an empty set, and the union of sets G, V, and S. Participants clarify the meanings of the symbols used, such as intersection and complement, and encourage the user to provide their work for further assistance. The conversation emphasizes understanding set operations to solve the given problems effectively.
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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