Question 1189241
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In a school of 970 students, all of them voted on two issues. 
390 students voted in favor of banning cell phones, and 930 students voted in favor of having a school dance. 
Just 20 students voted against both issues. How many students voted in favor of both proposals
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<pre>
In this problem, we have a universal set W of all 970 students.


We also have three subsets: B (banning) of 390 students;

                            D (dance)   of 930 students,

                   and      A (against both) of 20 students.


Notice that the sub-sets B and D may have non-empty intersection; while the sub-set A is DISJOINT from both B and D.


THEREFORE, the union of B and D has  970 - 20 = 950 students.


So, we can write  n(B U D) = n(B) + n(D) - n(B & D),  or

                     950   = 390  + 930 -  n(B & D).


From this equation, you get the <U>ANSWER</U> to the problem's question  n(B & D) = 390 + 930 - 950 = 370.


<U>ANSWER</U>.  370 students voted in favor of both proposals.
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Solved and thoroughly explained.