# How many are not taking a course in either computer science or in mathematics? Suppose that there are 1807 students at university. Of these, 453 are taking a course in computer science, 567 are...

How many are not taking a course in either computer science or in mathematics?

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Suppose that there are 1807 students at university. Of these, 453 are taking a course in computer science, 567 are taking a course in mathematics, and 299 are taking a courses in both computer science and mathematics.

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453 people took computer science i.e including those that took only computer science and mathematics. The same thing applies to the 567 people that took mathematics. To get the number of people that took only computer science we subtract 299 from 453 which gives 453 - 299 = 154 also to get the number of people that took only mathematics we subtract 299 from 567 which gives 567 - 299 = 268 the total number that took part in the survey is 1807. This number gives the total for those that took only computer science, mathematics, both mathematics and computer science and those that do not that both. I.e 1807 = 154 + 299 + 268 + x 1807 = 721 - x 1807 - 721 = x therefore x = 1086. Therefore the number that do not take part in either computer science and mathematics is 1086

the correct ans is

You have enough to find n(M U C) = n(M) + n(C) - n(M ∩ C). Those are the total of students who are taking either computer science or mathematics.

The remainder, 1807 minus that number, is the number who are taking neither.

You could work out those other counts too. 453 are taking computer science. 299 of those are also taking mathematics. So 453 - 299 are taking only computer science.

567 are taking mathematics. 299 of those are also taking computer science. So 567-299 are taking only mathematics.

Now you have the disjoint sets (math only), (computer science only) and (both math and computer science), and you could subtract those from 1807 to get (neither)