Question 1072460: Let the Universal set, S, have 169 elements. A and B are subsets of S. Set A has 80 elements, and set B has 75. If the total number of elements in A or B is 132, how many elements are in A, but not in B?
I have made a Venn Diagram, with 80 in A, and 75 in B. I am unsure how to figure out the problem from there. I have been working on it for over an hour now.
Thank you.
Found 3 solutions by MathTherapy, ikleyn, TeachMath:
Answer by MathTherapy(10552)   (Show Source):
You can put this solution on YOUR website!
Let the Universal set, S, have 169 elements. A and B are subsets of S. Set A has 80 elements, and set B has 75. If the total number of elements in A or B is 132, how many elements are in A, but not in B?
I have made a Venn Diagram, with 80 in A, and 75 in B. I am unsure how to figure out the problem from there. I have been working on it for over an hour now.
Thank you.
The 80 you have in A includes 57 in just A, but 23 in both A & B.
Therefore, elements in A, but not in B, or elements in just A, alone = 
Answer by ikleyn(52782)  (Show Source):
You can put this solution on YOUR website! .
The number of elements in the union A U B is
n(A U B) = n(A) + n(B) - n(A n B), (*)
where (A n B) symbolizes the intersection of A and B. By substituting the given data, you get
132 = 80 + 75 - n(A n B),
It implies n(A n B) = 80 + 75 - 132 = 155 - 132 = 23.
Thus you found out that the intersection (A n B) contains 23 elements.
Therefore, the number of elements that are in A, but not in B is 80 - 23 = 57.
Answer. The number of elements that are in A, but not in B is 57.
Regarding formula (*), see the lesson
- Counting elements in sub-sets of a given finite set
in this site.
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this online textbook under the topic
"Miscellaneous word problems".
Answer by TeachMath(96)  (Show Source):
You can put this solution on YOUR website! Let the Universal set, S, have 169 elements. A and B are subsets of S. Set A has 80 elements, and set B has 75. If the total number of elements in A or B is 132, how many elements are in A, but not in B?
I have made a Venn Diagram, with 80 in A, and 75 in B. I am unsure how to figure out the problem from there. I have been working on it for over an hour now.
Thank you.
Subset A has 57 elements that are NOT in subset B.
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