Venn Diagrams and Sets 07

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113 college students were surveyed and it was found out that all of them have visited at least one of the following three cities: Austin (TX), Boston (MA), and Chicago (IL).

66 of the students visited Austin.
52 of the students visited Boston.
76 of the students visited Chicago.
19 of the students visited Austin and Boston.
28 of the students visited Boston and Chicago.
42 of the students visited Austin and Chicago.
40 of the students visited exactly one of the following three cities: Austin, Boston, and Chicago.

a. How many students visited only Austin?
b. How many students visited only Boston?
c. How many students visited only Chicago?
d. How many students visited both Austin and Boston, but not Chicago?
e. How many students visited both Boston and Chicago, but not Austin?
f. How many students visited both Austin and Chicago, but not Boston?
g. How many students visited all of the following three cities: Austin, Boston, and Chicago?
Ans: a. 13, b. 13, c. 14, d. 11, e. 20, f. 34, g. 8