dmezzullo 2 years ago 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.

1. 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

2. brookie5150

@perl

3. perl

need help?

4. dmezzullo

yes perl help plz

5. perl

we know from Demorgans rule that \[(\sim H \cap \sim M )= (H \cup M ) ^{\sim}\]

6. dmezzullo

yes

7. perl

so we want Not (H union M) , and where does V intersect that. I get 15

8. perl

~ ( H U M ) is everything outside H union M. and V intersects that at 15 (where does V have it in common)

9. dmezzullo

what do u mean?

10. perl

we want \[V \cap (\sim H \cap \sim M )\\= V \cap (H \cup M ) ^{\sim}\]

11. dmezzullo

yes

12. perl

where does the circle V have in common with the region ~ ( H union M )

13. dmezzullo

9

14. perl

\[V \cap (\sim H \cap \sim M )\\= V \cap \sim (H \cup M ) \]

15. perl

we want the region outside H or M, so

16. perl

we are looking specifically at the area outside H or M

17. dmezzullo

1

18. perl

wait, first lets define what H union M is

19. dmezzullo

huh?

20. perl

U stands for union

21. dmezzullo

yes

22. perl

now we want the opposite , Not ( H union M )

23. perl

so that is the area outside

24. dmezzullo

ok

25. perl

now we want to know where Not ( H union M) intersects with circle V

26. dmezzullo

Ugh im so confused

27. perl

the answer is 15 by the way