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(52787)   (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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