Question 1190730: MAT 145: Topics In Contemporary Math
Sets and Set Operations
Given the definitions for the sets, find the elements in the subsets in roster notation.
Universal set U is the set of all letters in the English alphabet, A is set of all full-time
vowels (no y!), B is the set of the first 10 letters
A B 𝐴 ∩ B
𝐴 ∪ B A^c B^c
(𝐴 ∪ 𝐵)^c (𝐴 ∩ 𝐵)^c (𝐴 ∪ 𝐵) ∩ (𝐴 ∩ 𝐵)^c
𝐴 ∩ 𝐵^c 𝐴^c ∩ B 𝐴 ∩ A^c
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
U = universal set = set of all letters from English alphabet
U = {a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z}
A = set of vowels (no y)
A = {a,e,i,o,u}
B = first 10 letters
B = {a,b,c,d,e,f,g,h,i,j}
note how A and B are subsets of the universal set.
The union of A and B is the collection of stuff from A or from B (or both)
𝐴 ∪ B = {a,b,c,d,e,f,g,h,i,j,o,u}
Notice how we only list one unique letter without any repeats. This means you'll toss out any duplicates.
Sorting is optional but helpful.
The intersection of A and B is the set of what they have in common.
𝐴 ∩ B = {a,e,i}
B^c = set of stuff that isn't in B
B^c = {k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z}
In other words, it's the set of letters from k to z.
(𝐴 ∪ 𝐵)^c = set of stuff not in 𝐴 ∪ 𝐵
(𝐴 ∪ 𝐵)^c = {k,l,m,n,p,q,r,s,t,v,w,x,y,z}
basically we go from k to z but leave out the vowels o and u because they were found in 𝐴 ∪ B
I'll do one more but leave the rest for you to do
(𝐴 ∩ 𝐵)^c = set of stuff not in 𝐴 ∩ 𝐵
(𝐴 ∩ 𝐵)^c = {b,c,d,f,g,h,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z}
I started with the entire alphabet, then I kicked out letters a,e,i since they are found in 𝐴 ∩ 𝐵
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