# Set builder notation

A set can be described using symbols rather than words, for instance;
A = x : x < N, x < 6
This means that ‘A’ is the set of values of x such that x is a natural
number and x is less than 6. This notation is called set builder notation.
Such a set can be represented on a number line.
Example
Given that, B = x : x <R, 0 < x < 6 , where R is a Real number. Show
the solution set of B on a number line.
Solution
B is the set of real number x such that x is greater or equal to 0 and
less than 6. This can be represented on a number line as below

b) Write down the members of the following sets.
i) A
ii) B
iii) C
iv) A n C
c) Find:
i) n(A) + n(B) + n(C)
ii) n(A u B u C)

1. Given that n(A) = 22, n(B) = 22, n(A n B n C) = 5, n(A n B) = 11, n(C n A) =
7,n(B n C) = 9, and n(A u B u C) = 40. Find n(C).
2. A certain class was asked whether they liked science and history. Twice
as many liked science as liked history. Eight said they liked both
subjects and nine pupils said they did not like either subject. If there
were 46 pupils in the class, use a Venn diagram to work out how many
pupils liked science.
1. In a form 3 class, the teacher told the students to bring a pen, a pencil,
and a ruler to class. The following day, she found that of the 40
students, only 12 had brought all the three instruments, 5 students
didn’t have any at all. 11 students did not have a pen, 12 students did
not have a pencil, and 18 students did not have a ruler. One student
ruler.
a) Draw a Venn diagram to illustrate this information and find out how
many students had at least a pencil and a ruler.
b) The students who had less than two instruments were put in
detention. How many students were put in detention?
Book 2
15
Mathematics simplified
2. In a certain school, a sample of 100 students were picked randomly. In this sample, it was found out that 78 students play netball (N), 82 play volleyball (V), 53 play tennis (T) and 2 do not play any of the three games. All those that play tennis also play volleyball. 48 play all the three games.
a) Represent the given information on a Venn diagram.
b) How many students play both netball and volleyball but not tennis?
3. Of the 80 senor five students that passed Math (M) in Negri College Gulu; 45 passed Physics (P), 60 passed Chemistry (C), 5 passed Biology (B) and M only, 5 passed M only. Those who passed P, C, B, and M equal to those who passed only B, C, and M. The number of students who passed M and C only equal to those who passed M, B, and P only and are 5 less than those who passed all the 4 subjects.
a) Represent the above information on a Venn diagram.
b) Find the number of those who passed:
i) all the four Subjects.
ii) only three subjects.
c) A student is selected at random. Find the probability that the student;
i) passed by 2 subjects.
ii) did not pass Biology.