Question 1198452
A survey asked 1000 college students which courses they were taking this semester. The survey obtained the following information: 

- 347 are taking a Math course
- 343 are taking a English course
- 39 are taking both a Science and a English course
- 8 are taking a Math course, a Science course, and a English course
- 65 are taking both a Math and a English course
- 758 are taking a Science course or a English course
- 221 are taking a Math course but not a Science course nor a English course

a.) use the information listed to complete a three-circle venn diagram M,E,and S.

b.) using the results from the venn diagram in question a.), determine how many students:

i.) are taking a science course:
ii.) are taking an English course but not a Math course: 
iii.) are not taking a Math course
iv.) are taking at least two of the types of courses (Math, English and Science)
<pre>As requested, numbers that are taking math, science, and english are M, S, and E, respectively
We find that number that take:	math only, is: M, only
				science only, is: S, only
				english only, is: E, only
					
				math and science, only, is: M&S
				math and english, only, is: M&E

				science and english, only, is: S&E
				math, science, and english, is: M&S&E
					
The VENN DIAGRAM below has been labeled as such.
*[illustration ADC_1198452.png].

M   = M, only + M&E + M&S&E + M&S
347 = 221 + 57 + 8 + M&S ------ Substituting 347 for M, 221 for M, only, 57 for M&E, and 8 for M&S&E
347 = 286 + M&S
347 - 286 = M&S
61 = M&S

E = 343, so E, only += 343 - (31 + 8 + 57) = 343 - 96 = 247

S or E = S, only + S&E + E, only + M&S&E + M&S + M&E
   758 = S, only + 31  +   247   +   8   +  61 + 57 
   758 = S, only + 404
758 - 404 = S, only
      354 = S, only

We now get the following VENN DIAGRAM with all variables’ values entered
  *[illustration ADC_1198452_21.png].
I’ll start you off with: How many i.) are taking a science course:
                                               S = S, only + S&E + M&S&E + M&S 
S, or number of students taking a science course =   354   + 31  +   8   +  61 = <font color = red><font size = 4><b>454</font></font></b></pre>