Sets questions | form five Pure Advanced Mathematics

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

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?

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?

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

1. Use the laws of algebra to simplify

2. Out of a group of 17 girl guides and 15 boy scouts, 22 play handball, 16 play basketball, 12 of the boy scouts play handball, 11 of the boy scouts play basketball, 10 of the boy scouts play both and 3 of the girl play neither of the two .

1. How many girls play both handball and basketball?
2. How many in the group play handball only and basketball only?

Simplify A-(A-B) using properties of sets.

In a survey of 500 movie viewers , 250 were listed as liking ‘zecomedy’, 200asliking ‘zembwela’ and 85 were listed as liking both ‘zecomedy’ as well as ‘zembwela’. Using the appropriate formula, find how many people were liking neither zecomedy nor zembwela.

If sets A and B are defined by and , find A-B in the same set notation.

Use laws of algebra of sets to simplify .

In a class of 17 girls and 15 boys, 22 play handball, 16 play basketball, 12 of the boys play handball, 11 of the boys play basketball, 10 of the boys play both basketball and handball, 3 of the girls play neither of the two games. Use Venn diagram to determine;

1. the number of girls who play both games and
2. the number of participants who play at least one game.