Question 1182919: I have been struggling with this problem for a few days now:
Let
U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A = {1, 2, 4, 6}
B = {3, 7}
C = {1, 3, 6, 7, 9}
List all the members of the following set.
A ∩ (B ∪ C)
The class I am taking has no textbooks to reference, so I have been trying to figure this out on my own. I found a similar question with a similar set (where the places of A and C were swapped in the set) on this website, and so I tried the solution and got this as my final answer:
3,6,7
The solution basically suggested that you combine the numbers and drop all duplicates (the solution I followed ignores all members of U and only used A, B, and C members).
The answer, however, is incorrect.
I am stumped and would appreciate any tips. Thank you!
So
Found 4 solutions by MathLover1, helper 1234321, ikleyn, MathTherapy:
Answer by MathLover1(20850)   (Show Source):
You can put this solution on YOUR website!
U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A = {1, 2, 4, 6}
B = {3, 7}
C = {1, 3, 6, 7, 9}
List all the members of the following set.
A ∩ (B ∪ C)
fits find (B ∪ C), all members of the set B or C
(B ∪ C)={1, 3, 6, 7, 9}=C
then
recall: 
so,
A ∩ (B ∪ C)={1, 2, 4, 6}∩{1, 3, 6, 7, 9}...only common members
A ∩ (B ∪ C)={1,6}
Answer by helper 1234321(1)  (Show Source):
Answer by ikleyn(52879)  (Show Source):
You can put this solution on YOUR website! .
I have been struggling with this problem for a few days now:
Let
U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A = {1, 2, 4, 6}
B = {3, 7}
C = {1, 3, 6, 7, 9}
List all the members of the following set.
A ∩ (B ∪ C)
The class I am taking has no textbooks to reference, so I have been trying to figure this out on my own. I found a similar question with a similar set (where the places of A and C were swapped in the set) on this website, and so I tried the solution and got this as my final answer:
3,6,7
The solution basically suggested that you combine the numbers and drop all duplicates (the solution I followed ignores all members of U and only used A, B, and C members).
The answer, however, is incorrect.
I am stumped and would appreciate any tips. Thank you!
So
~~~~~~~~~~~~
The symbol B U C denotes the UNION of two subsets B and C of the universal set U.
The union is the list of all elements belonging to B or C; if some element does belong to both B and C,
we list it ONLY ONCE in the union.
So, the union (B U C) is this set {1, 3, 6, 7, 9}.
NEXT, we take the INTERSECTION A ∩ (B ∪ C).
This intersection is the subset, containing elements, common to A and to (B U C).
We list each common element ONLY ONE TIME in the intersection.
So, the intersection is
A ∩ (B ∪ C) = {1, 6}.
ANSWER. A ∩ (B ∪ C) = {1, 6}.
Solved, answered and carefully explained.
Answer by MathTherapy(10556)  (Show Source):
You can put this solution on YOUR website!
I have been struggling with this problem for a few days now:
Let
U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A = {1, 2, 4, 6}
B = {3, 7}
C = {1, 3, 6, 7, 9}
List all the members of the following set.
A ∩ (B ∪ C)
The class I am taking has no textbooks to reference, so I have been trying to figure this out on my own. I found a similar question with a similar set (where the places of A and C were swapped in the set) on this website, and so I tried the solution and got this as my final answer:
3,6,7
The solution basically suggested that you combine the numbers and drop all duplicates (the solution I followed ignores all members of U and only used A, B, and C members).
The answer, however, is incorrect.
I am stumped and would appreciate any tips. Thank you!
So
Yes, elements in set U are NOT factored into your answer for: A ∩ (B ∪ C)
A ∩ (B ∪ C)
∪ INDICATES UNION, which is: ALL ELEMENTS in BOTH sets, EXCLUDING DUPLICATES
A ∩ [B + C - (B ∩ C)]
A ∩ (ALL in BOTH sets, or ALL in B & C, EXCLUDING DUPLICATES)
A ∩ (ALL in B + ALL in C, less ELEMENTS in BOTH B & C)
(1, 2, 4, 6) ∩ [(3, 7) + (1, 3, 6, 7, 9) - (3, 7)]
(1, 2, 4, 6) ∩ (1, 3, 6, 7, 9)
A ∩ (B ∪ C) = 
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