Science Anyone?

A survey was taken of students at the university concerning their enrollment in liberal arts courses. Each of 600 students was asked to answer yes or no to each of the questions:

Are you enrolled in a humanities course?

Are you enrolled in a natural science course?

Are you enrolled in a social science course?

So far the following data from the survey have been tabulated.

250 of the students survey are enrolled in natural science courses

100 are enrolled both in a humanities course and a social science course

130 are enrolled in a natural science course but not in a humanities course

120 are enrolled only in a social science course

30 are enrolled in all three course areas

270 are enrolled in a social science course

300 are enrolled in only one of the three areas

The dean of liberal arts is interested in know the answers to the questions.

a) How many of the students surveyed are enrolled in none of these three areas?

b) How many of the student surveyed are enrolled in at least one of the three areas?

c) How many of the students surveyed are enrolled in at least two of the three areas?

d) How many of the students survey are enrolled in a humanities course?

Flawed Data

A sociologist surveyed 100 college students and came up with these data:

72 own cars

60 own stereos

20 own both items.

On seeing these results, another sociologist claimed that the doing the survey was either a fraud or incompetent (or both). Is this correct? Why?