8. In a school there are 20 teachers who teach mathematics or physics. Of these 12 teach mathematics and 4 teach both physics and mathematics. How many teach physics?

9. There are 200 individuals with a skin disorder, 120 had been exposed to the chemical C1, 50 to chemical C2, and 30 to both the chemicals C1 and C2. Find the number of individuals exposed to

(1) chemical C1 but not chemical C2

(2) chemical C2 but not chemical C1

(4) chemical C1 or chemical C2

10. In a survey it was found that 21 peoples liked product A, 26 liked product B and 29 liked product C. If 14 people liked products A and B, 12 people like C and A, 14 people like B and C and 8 liked all the three products. Find now many liked product C only.

7. For any two sets A and B prove by using properties of sets that: (A B A - B = A ∩ ∪) ( )

8. If A, B, and C, are three sets and U is the universe set such that n(U) = 1000, n(A) = 300, n (B) 300 and n(A∩ B) = 200 find n (A B ′ ′ ∩ ) . 9. A college awarded 38 medals in football, 15 in basketball and 20 in cricket. If these medals went to a total of 58 men and only three men got medal in all the three sports, how many received medals in exactly two of the three sports? 10. In a survey of 60 people, it was found that 25 people read news paper H, 26 read newspaper T, 26 read newspaper I, 9 read both H and I, 11 read both H and T, 8 read both T and I, 3 read all three newspaper. Find (i) The no. of people who read at least one of the newspapers. (ii) The no. of people who read exactly one news paper.

6. There are 210 members in a club. 100 of them drink tea...

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