Sets questions | form five Pure Advanced Mathematics

In a town of 10000 families , it was found that 40% families buy Mwananchi , 20% families buy Mwanahalisi and 10% buy Raia mwema, 5% families buy Mwananchi and Mwanahalisi, 3% buy Mwanahalisi and Raia mwema, 4% buy Mwananchi and Raia mwema.If 2% families buy all three newspapers in town, Find the number of families that buy:

1. Mwananchi only
2. Mwanahalisi only
3. Non of the three newspapers in town.

Without drawing Venn diagram

Simplify using the laws of algebra of sets (AnB)U(A-B)

At MTAKUJA secondary school, 48 students study physics, Mathematics or chemistry. Out of these 35 study physics, 12 study physics and chemistry, 8 study mathematics ,5 study physics and mathematics. All who study mathematics also study physics and chemistry. Those who study physics only are twice as much as those who study chemistry only. Find the number of students studying 

• Chemisrty and physics but not mathematics
• Physics only
• chemistry

Using the laws of algebra proportion of sets simplify

[(AnB)U(AnB')U(A'nB)U(A'nB')]

In a battle involving a hundred , 42 were shot on the head , 43 on the arm, 32 on the leg, 5 on the head and arm, 8 on the arm and leg, 6 on the leg and head. How many were shot on all 3 parts?

Simplify

• (AnB^c)U(AUB^c)
• (A-B)U(A-C)
• (AUB)^cU(AnB)^c

In a certain class 15 girls like to dance, 5 like to play football and 6 are singers. Every footballer in their class like dancing . 2 girls are both footballers and singers. 3 singers do not like dancing . Find

• The number of girls in a class
• The number of girls who are singers and not footballers.

Use the laws of algebra of sets to simplify the following:

1. [An(A'UB)] U [Bn(A'UB')]
2. [(AnB)U(AnB')U(A'nB')]'

At jagwani Secondary school , thirth five students are taking economics, those who take mathematics are two-third of those who take economics and geography. Those who take economics only are twice of those who take geography only. All who take mathematics take economics or geography.Forty eight students take mathematics or economics or geography. Those who take economics and mathematics are one seventh as many as those who take economics. Those who take economics and geography are one quarter of those who take economics or geography or mathematics.

By using Venn diagram find the number of students who are taking

1. At most two subjects
2. Geography and mathematics but not economics
3. Mathematics or or economics but not geography
4. At least two subjects 

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).