In a survey of the dining preferences of 110 dormitory students at the end of the spring semester, the following facts were discovered about Adam's Lunch AL, Pizza Tower PT, and the Dining Hall DH. 15 liked AL but not PT 10 liked AL only 23 liked AlL 42 liked PT 48 liked DH 4 liked PT and AL but not DH 25 liked PT and DH How many liked PT or DH? 0 27 O 39 O 25 O 52 O 65

The result of the survey that shows the set of the students preferences can

be represented with a Venn diagram.

Reasons:

The number of students = 110

15 liked AL but not PT = |AL ∩ PT'|

10 liked AL only = |AL ∩ PT' ∩ DH'|

23 liked AL = n|AL|

42 liked PT = n|PT|

48 liked DH = n|DH|

4 liked PT and AL but not DH  = |PT ∩ AL ∩ DH'|

Number that liked PT and DH = 25 = |PT ∩ DH|

Required:

The number that liked PT or DH

Therefore;

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65 Dormitory Students

Step-by-step explanation:

Given

15 liked AL but not PT

10 liked AL only

23 liked AL

42 liked PT

48 liked DH

4 liked PT and AL but not DH

25 liked PT and DH

How many likes PT or DH?

This can be represented by n(PT u DH)

n(PT U DH) = Number of those that like PT or DH

n(PT U DH) = n(PT) + n(DH) - n(PT n DH)

Where n(PT) = Number of those that like PT = 42

n(DH) = Number of those that like DH = 48

n(PT n DH) = Number of those that like PT and DH = 25

So, we have

n(PT U DH) = 42 + 48 - 25

n(PT U DH) = 65