Question

A survey was conducted among 78 patients admitted to a hospital cardiac unit during a​ two-week period. The data of the survey are shown below. Let B equals the set of patients with high blood pressure. Let C equals the set of patients with high cholesterol levels. Let S equals the set of patients who smoke cigarettes.​n(B) equals 36 ​n(B intersect​ S) equals 10 ​n(C) equals 34 ​n(B intersect​ C) equals 12 ​n(S) equals 30 ​n(B intersect C intersect​S) equals 5 ​n[(B intersect​ C) union​ (B intersect​ S) union​ (C intersect​ S)] equals 21

Answer 1

Sets and set operations are ways of organizing, classifying and obtaining information about objects according to the characteristics they possess, as objects generally have several characteristics, the same object can belong to several sets, an example is the subjects of a school , where students (objects) are classified according to the subject they study (set).

The intersection of sets is a new set consisting of those objects that simultaneously possess the characteristics of each intersected set, the intersection of two subjects will be those students who have both subjects enrolled.

The union of sets is a new set consisting of all the objects belonging to the united sets, the union of two subjects will be all students of both courses.

In this case there are three sets B, C and S of which we are given the following information:

Answer

n(BꓵSꓵC)=5

n(BꓵS)=10 – 5 = 5

n(BꓵC)=12 – 5 = 7

n[(BꓵC)ꓴ(BꓵS)ꓴ(CꓵS)]=21  – 5 – 5 – 7 = 4

n(B)=36 – 5 – 5 – 7 = 19

n(S)=30 – 5 – 5 – 4 = 16

n(C)=34 – 5 – 7 – 4 = 18