Of the 300 students in 8th grade, 180 take PE, 80 take art. 72 take music, 33 take PE and art, 28 take PE and music, and 20 take all three
classes
M= all students taking music
A= all students taking art
P= all students taking PE
Which of the sets has more than 150 students? Select all that apply
AUM
POM
PNAM
PUAUM
1- (PNA)

The sets has more than 150 students

P∪A∪M

-(P∩A)

Step-by-step explanation:

See the attached figure which represents Venn diagram for the question:

180 take PE

80 take art

72 take music

33 take PE and art

28 take PE and music

20 take all three

M= all students taking music

A= all students taking art

P= all students taking PE

Number of students taking PE and art only = 33 - 20 = 13

Number of students taking PE and music only = 28 - 20 = 8

Number of students taking PE only = 180 - (20 + 13 + 8) = 139

Number of students taking ARt only = 80 - (20 + 13) = 47

Number of students taking Music only = 72 - (20 + 8) = 44

Number of students doesn't take any thing =

300 - (20 + 13 + 8 + 139 + 47 + 44) = 29

We will check the options to find the sets has more than 150 students:

1)  A∪M = 13 + 47 + 20 + 8 + 44 = 132 < 150

2) P∩M = 20 + 8 = 28 < 150

3) P∩A∩M = 20 < 150

4) P∪A∪M = 20 + 13 + 8 + 139 + 47 + 44 = 271 > 150

5) -(P∩A) = 300 - (13+20) = 267 > 150

So, The sets has more than 150 students

P∪A∪M

-(P∩A)

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