Question

A survey was completed by individuals who were currently on the Zone diet (Z), the South Beach diet (S), or the Weight Watchers diet (w). All persons surveyed were also asked whether they were currently in an exercise program (E), taking diet pills (P), or under medical supervision (M). The following table shows the results of the survey. Supplements Totals z 124 83 63 270 Diet S 105 63 51 219 W 134 44 43 221 Totals363 190 157 710 Find the number of surveyed people in each of the following sets. (a) SnE 105 people (b) ZUM 63 people (c) Sin (EUP) 385 people (d) (ZUS) n (M) 375 people (e) W'n (PUM)' people

I do not understand how to get a union of something such as Z U M, and I have trouble also when it comes to Complements and multiple parentheses. What is the step-by-step way of solving each of these parts of the problem, and why is it set up the way it is?

Answer 1

(P U M) = 190+157 = 347

(P U M)' = 363

W' = 270+221 = 491

W' ∩ (P U M)' = 124+105 = 229