A group of 368 students were surveyed about the courses they were taking at their college
with the following results:
145 students said they were taking Math.
223 students said they were taking English.
225 students said they were taking History.
92 students said they were taking Math and English.
98 students said they were taking Math and History.
159 students said they were taking English and History.
80 students said they were taking all three courses.
How many students took English and History, but not Math?
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UpStudy AI · Accepted Answer

Let $$ E $$ be the set of students taking English and $$ H $$ be the set of students taking History. The survey tells us that

$$
|E \cap H| = 159
$$

and that

$$
|M \cap E \cap H| = 80,
$$

where $$ M $$ represents students taking Math.

We want to find the number of students taking English and History but not Math, which can be written as

$$
|E \cap H \setminus M|.
$$

This is calculated by subtracting the number of students taking all three courses from the students taking both English and History:

$$
|E \cap H \setminus M| = |E \cap H| - |M \cap E \cap H|.
$$

Substitute the given numbers:

$$
|E \cap H \setminus M| = 159 - 80 = 79.
$$

Thus, $$79$$ students took English and History, but not Math.
79 students took English and History, but not Math.

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