Sets questions | form five Pure Advanced Mathematics

Three sets A,B,C are defined as follows:

A={X:2 <X<=5}

B={X:X<=2}

C={X;-2<=X<3}

Sketch the following sets on a number line.

1. AUB^c
2. A^cnB
3. A^c n(BUA).

Answer / Solution

UNSOLVED

At Mkandawile High school, 128 students were interviewed , 8 students didn't like maths or chemistry.The number of students who liked Maths only was three times those who liked chemistry only. Furthermore the number of students who liked chemistry was half the number of students who likde maths. Find the number of students who liked 

1. Math only
2. Both maths and chemistry

Answer / Solution

UNSOLVED

1. Use the appropriate laws to simplify (An(AuB)’)’.
2. A certain farmer who produces 3 types of food crops: maize , beans and millet conducted a survey of 205 families. The following were the findings: 82 use maize, 110 use beans, 73 use millet, 59 use beans and millet, 32 use maize and millet and 20 use all products. How many of the interviewed families use none of these products?

Answer / Solution

UNSOLVED

1. Simplify giving reasons the statement
2. One poultry farm in Dar es salaam which produces three types of chicks, had its six-month report which revealed that out of 126 of its regular customers , 65 bought broilers, 80 bought layers and 75 bought cocks. 45 bought layers and cocks, 35 bought broilers and cocks, 10 bought broilers only, 15 bought layers only and 6 bought cocks only. 6 of the customers did not show up.

1. How many customers bought all three products?
2. How many customers bought exactly two of the farm`s products?

Answer / Solution

UNSOLVED

1. Use the algebra of sets to simplify
2. Out of 150 deaths of children that occured at Mamboleo Village over a period of 5 years , 60% were caused by diarrhoea, 30% by malaria and 40% by pneumonia. The deaths caused by diarrhoea and malaria were 18 by diarrhoea and pneumonia were 30 and by malaria or pneumonia but not diarrhoea were 51. The number of children who died because of all was 12. Find the number of children whose deaths were caused by:

1. diseases other than the three mentioned above
2. diarrhoea or pneumonia but not malaria

Answer / Solution

UNSOLVED