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# How many are taking neither subject?

There are 23 students in a classroom. 18 are taking math and 15 are taking science. Six students are taking math but not science.

Are there students in the class that are taking neither math nor science?
The information given comes up with 6 taking math only, 12 taking both,
3 taking science only... but that only accounts for 21 students.  This leaves
2 students unaccounted for.
Disregard above comment... Heading above problem states it.

### 1 Answer by Expert Tutors

Andrew M. | Mathematics - Algebra a Specialty / F.I.T. Grad - B.S. w/HonorsMathematics - Algebra a Specialty / F.I....
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If you draw two intersecting circles for a Venn Diagram

You have 3 areas...   The intersecting area in the middle is
for students taking both math and science.  The left circle
label math.  The right circle label science.  The middle area
label both.

Putting a 6 in the area for math only leaves 12 to put
in the area for taking both.
That means there are 3 taking science only to make the
15 that take science.
So we have:

Math only ...    6
Science only... 3
Both ...           12
------
21

Since we have 23 students, 2 students take neither math nor science.