dmezzullo
  • dmezzullo
Campbell Music Academy held workshops on classical music composers Mozart, Vivaldi, and Haydn. The Venn diagram shows the number of seniors who chose to attend workshops on each of the three composers.
Mathematics
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SOLVED
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jamiebookeater
  • jamiebookeater
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dmezzullo
  • dmezzullo
If the total number of seniors in the academy is 64, what is the total number of students who belong to the set V ∩ (~H ∩ ~ M)? 45 33 19 15
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anonymous
  • anonymous
@perl
perl
  • perl
need help?

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dmezzullo
  • dmezzullo
yes perl help plz
perl
  • perl
we know from Demorgans rule that \[(\sim H \cap \sim M )= (H \cup M ) ^{\sim}\]
dmezzullo
  • dmezzullo
yes
perl
  • perl
so we want Not (H union M) , and where does V intersect that. I get 15
perl
  • perl
~ ( H U M ) is everything outside H union M. and V intersects that at 15 (where does V have it in common)
dmezzullo
  • dmezzullo
what do u mean?
perl
  • perl
we want \[V \cap (\sim H \cap \sim M )\\= V \cap (H \cup M ) ^{\sim}\]
dmezzullo
  • dmezzullo
yes
perl
  • perl
where does the circle V have in common with the region ~ ( H union M )
dmezzullo
  • dmezzullo
9
perl
  • perl
\[V \cap (\sim H \cap \sim M )\\= V \cap \sim (H \cup M ) \]
perl
  • perl
we want the region outside H or M, so
perl
  • perl
we are looking specifically at the area outside H or M
dmezzullo
  • dmezzullo
1
perl
  • perl
wait, first lets define what H union M is
dmezzullo
  • dmezzullo
huh?
perl
  • perl
U stands for union
dmezzullo
  • dmezzullo
yes
perl
  • perl
now we want the opposite , Not ( H union M )
perl
  • perl
so that is the area outside
dmezzullo
  • dmezzullo
ok
perl
  • perl
now we want to know where Not ( H union M) intersects with circle V
dmezzullo
  • dmezzullo
Ugh im so confused
perl
  • perl
the answer is 15 by the way

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