a) none of the 3 b) only math 111 c) ins 111 and eng 111 and not math 111 d) only one course e) only 2 courses

(a)

The Venn diagram helps to solve this type of problem. Here's the key:

A=Commerce students who didn't take any of the 3 subjects.

B=Ins only students

C=Math only

D=Eng only

E=Ins+Eng only

F=Math+Eng only

G=Ins+Math only

H=All 3

Now some figures:

A+B+C+D+E+F+G+H=120

B+E+G+H=38

D+E+F+H=36

C+F+G+H=100

E+H=26

F+H=22

G+H=26

H=18

So, E=8, F=4, G=8.

C=100-(4+8+18)=70

D=36-(8+4+18)=6

B=38-(8+8+18)=4

A=120-(4+70+6+8+4+8+18)=2

(a) A=2 students took none of the 3

(b) C=70 students took math only

(c) E=8 students took ins and eng only

(d) B+C+D=80 students took only one course

(e) E+F+G=20 students took only two courses

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