# Stuck on Venn Diagram Problem

#### dizzieko03

##### New member
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

##### Well-known member
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,

#### ZaidAlyafey

##### Well-known member
MHB Math Helper
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

Staff member
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!

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.