Question 1182920: (UPDATED / DUPLICATE!!!!! I submitted this question but forgot to add a major detail about my what I had tried!
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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). After dropping all duplicates, the solution suggested you also drop any numbers that are NOT included in A, B, AND C.
The answer, however, is incorrect.
I am stumped and would appreciate any tips. Thank you!
Found 2 solutions by ewatrrr, ikleyn:
Answer by ewatrrr(24785)   (Show Source):
You can put this solution on YOUR website! 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)
(B ∪ C) |Union: B & C all together ..no dups: {1,3,6,7,9}
A ∩ (B ∪ C) \ Intersection: only what they have in common:
{1, 2, 4, 6} ∩ {1,3,6,7,9}
Which is {1.6}
Answer by ikleyn(52781)  (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
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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.
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