Topic 13: Set Theory – Sample Activity

Context

Set Theory In Vitera village, many children die before the age of 5. A survey by doctors indicates that the children die with signs and symptoms of either bacterial sinusitis, skin infection or cough.

Support Material

Of the 92 children who died last year, 71 had skin infection (S), 72 had bacterial sinusitis (B) and 45 had cough (C). 51 had S and B, 39 had S and C while 36 had C and B

Task

Interpret the information onto a Venn diagram to guide the doctors while planning for medical intervention for Vitera village.

Topic Summary

In this topic, you have learnt that:

• a set is comprised of related items.
• a set is described by the related members found within it. For example, A = {2, 4, 6, 8, 10, 12} can be described as a set of the first six even numbers OR even numbers between 1 and 13.
• disjoint sets are two sets with no members in common.
• the number of elements in set A is denoted as n(A) and is obtained by counting the elements that make set A.
• a Venn diagram is very helpful in the representation of sets and in solving real-life problems involving sets.

Revision Exercise

1. Given that G is the set consisting of whole numbers less than 20.

a) Write down the set consisting of 1.

(i) even numbers. 2.

(ii) odd numbers.

(iii) prime numbers.

(iv) triangular numbers.

(v) the set consisting of intersection of odd numbers and prime numbers

2. Draw a Venn diagram showing the intersection of (ii) and (iii). The diagram shows the books on a shelf in the library where Mathematics books (M), English books(E) and both Mathematics and English books are mixed

Find the total number of:

(a) books on the book shelf.

(b) (i) only Mathematics books on the book shelf.

(ii) only English books on the book shelf.

3. The diagram shows the number of learners who prefer studying English (E), Geography (G) and Mathematics (M). Other learners prefer studying subjects other than English or Geography or Mathematics.

(a) Find the total number of learners in the school.

(b) Find the total number of learners who prefer studying

(i) Mathematics.

(ii) English.

(iii) Mathematics and Geography.

(iv) English and Geography only.

(c) Calculate the total number of learners who like studying only one subject.