Sets questions | form five Pure Advanced Mathematics

In her birth day Habari invited a total of 39 people. At the end of the function it was reported that 17 bottles of Sayona, 18 bottles of Fanta and 21 bottles of Coca Cola were used . If 5 people were diabetic and did not take any drink containing sugar. How many people in the function took all the three beverages if 9 took both Sayona and Fanta, 7 took Fanta and Coca cola and 19 again took Sayona and Coca cola.

Using the basic properties of sets operations, simplify each of the following expressions;

1. (AnB')U(A'nB)U(AnB)
2. (AuB)n(A'UB)n(AUB')n(A'UB')

In a survey of 60 students in a certain school it was found that

25 study physics, 26 study mathematics, 26 study chemistry, 9 study both physics and chemistry, 11 study both physics and mathematics , 8 both mathematics and chemistry, 3 study all subjects.

Represent this information by using a suitable venn diagram. From the diagram find the number of students who

• study exactly one subject
• study none of the subjects

Given that n(AnB)=9, n(A-B)=11,  n(AUB)=27 and n[AnB]'=21

Find:

1. n(A)
2. n[(AUB)']
3. n(A'nB)

A certain farmer who produces 3 types of food crops: maize, beans and millet conducteda survey of 220 families. The following were the findings:

105 families use maize, 126 use beans, 106 use millet, 61 use maize and beans, 49 use maize and millet, 100 use millet or beans but not maize and 25 use all three crops. How many of the families interviewed  use:

1. None of these crops
2. Exactly two food crops

Using the basic properties of set operation, simplify each of the following expressions.

1. (AnB')U(AUB')
2. (AnB)U(A'nB)U(AnB')

In a class of 35 students , each student takes either one or two language subjects(English, literature and Kiswahili). If 13 students take literature, 22 students take English, 17 students take Kiswahili, 6 students take both language and literature, 3 students take both Kiswahili and literature, find the number of students who take

1. Both Kiswahili and English
2. Just one subject
3. Literature but not English

Define disjoint of two sets A and B.

Use the laws of algebra of sets to show that AB and B are disjoint.

Out of 20 teachers in a school , 10 teach mathematics, 9 teach physics and 7 teach chemistry, 4 teach mathematics and physics, but none teaches both mathematics and chemistry. Show this information in Venn diagrams , then find :

• The number of teachers who teach chemistry and physics
• The number of teachers who teach physics only.

If A ,B and C are any three sets, then

prove that A-(BnC)=(A-B)U(AUC)