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.
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dmezzullo
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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
brookie5150
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@perl
perl
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need help?
dmezzullo
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yes perl help plz
perl
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we know from Demorgans rule that
\[(\sim H \cap \sim M )= (H \cup M ) ^{\sim}\]
dmezzullo
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yes
perl
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so we want Not (H union M) , and where does V intersect that. I get 15
perl
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~ ( H U M ) is everything outside H union M. and V intersects that at 15 (where does V have it in common)
dmezzullo
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what do u mean?
perl
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we want \[V \cap (\sim H \cap \sim M )\\= V \cap (H \cup M ) ^{\sim}\]
dmezzullo
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yes
perl
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where does the circle V have in common with the region ~ ( H union M )
dmezzullo
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9
perl
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\[V \cap (\sim H \cap \sim M )\\= V \cap \sim (H \cup M ) \]
perl
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we want the region outside H or M, so
perl
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we are looking specifically at the area outside H or M
dmezzullo
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1
perl
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wait, first lets define what H union M is
dmezzullo
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huh?
perl
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U stands for union
dmezzullo
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yes
perl
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now we want the opposite , Not ( H union M )
perl
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so that is the area outside
dmezzullo
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ok
perl
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now we want to know where Not ( H union M) intersects with circle V
dmezzullo
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Ugh im so confused
perl
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the answer is 15 by the way