How Do You Solve Complex Venn Diagram Problems Involving Sets?

[dizzieko03]

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)

 

[Petrus]

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,

 

[alyafey22]

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 .

 

[MarkFL]

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.

 

[blue_raver22]

’

Hi there,

I understand that you are struggling with a Venn diagram problem. Venn diagrams are visual representations of sets and their relationships. To solve this problem, we will first need to understand the given sets.

The universal set is the set of all lower case English letters. This means that any letter in the English alphabet can be included in this set.

The set V represents the vowels in the English alphabet. This includes the letters a, e, i, o, and u.

The set S represents the letters in the word "spring". This includes the letters s, p, r, i, and n.

The set G represents the letters in the word "garden". This includes the letters g, a, r, d, e, and n.

Now, let's look at the operations that need to be performed.

a. G' ∩ V - This operation means finding the intersection of the complement of set G and set V. The complement of set G would be all the letters in the universal set that are not in set G. So, G' would be {b, c, f, h, j, k, l, m, n, o, p, q, s, t, u, v, w, x, y, z}. The intersection of G' and V would be the letters that are common in both sets, which in this case would be {a}.

b. (G ∩ V) ∩ { } - In this operation, we first find the intersection of sets G and V, which would be {a}. Then, we need to find the intersection of this result with an empty set, which would be an empty set itself.

c. (G ∪ V ∪ S)' - This operation means finding the complement of the union of sets G, V, and S. The union of these sets would be {a, e, i, o, u, s, p, r, n, g, d}. The complement of this set would be all the letters in the universal set that are not in this set. So, the result would be {b, c, f, h, j, k, l, m, q, t, v, w, x, y, z}.

I hope this breakdown helps you understand how to solve this Venn diagram problem. If you have any further questions, please feel free to ask. Good luck!