#### Term 2 Set Language Five Marks Questions

9th Standard

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Maths

Time : 01:00:00 Hrs
Total Marks : 50
10 x 5 = 50
1. Using the adjacent Venn diagram, find the following sets:
(i) A-B
(ii) B-C
(iii) A'$\cup$B')
(iii) A'$\cap$B'
(iv) (B$\cup$C)'
(vi) A-(B$\cup$C)
(vii) A-(B$\cap$C)

2. If A, B and C are overlapping sets, then draw Venn diagram for the following sets:
(i) (A-B)$\cap$C
(ii) (A$\cup$C)-B
(iii) A-(A$\cap$C)
(iv) (B$\cup$C)-A
(v) A$\cap$B$\cap$C

3. If A = {x : x = 6n, n$\in$W and n<6}, B = {x:x = 2n, n $\in$N and 2 < n ≤ 9} and C = {x:x = 3n, n$\in$N and 4n ≤ n < 10}, then show that $A-(B\cap C)=(A-B)\cup (A-C)$.

4. If A={y:y=$\frac { a+1 }{ 2 }$, a $\in$ W and a≤5}, B={y:y=$\frac { 2n-1 }{ 2 }$, n$\in$W and n<5} and C=$\left\{ -1,-\frac { 1 }{ 2 } ,1,\frac { 3 }{ 2 } ,2 \right\}$, then show that $A-(B\cup C)=(A-B)\cap (A-C)$.

5. Verify $n\left( A\cup B\cup C \right) =n(A)+n(B)+n(C)-n(A\cap B)-n(B\cap C)-n(A\cap C)+n(A\cap B\cap C)$for the following sets.
(i) A = {a, c, e, f , h} , B = {c, d, e, f } and C = {a, b, c, f }
(ii) A = {1, 3, 5} , B = {2, 3, 5, 6} and C = {1, 5, 6, 7}

6. In a colony, 275 families buy Tamil newspaper, 150 families buy English newspaper, 45 families buy Hindi newspaper, 125 families buy Tamil and English newspapers, 17 families buy English and Hindi newspapers, 5 families buy Tamil and Hindi newspapers and 3 families buy all the three newspapers. If each family buy atleast one of these newspapers then find.
(i) Number of families buy only one newspaper.
(ii) Number of families buy atleast two newspapers.
(iii) Total number of families in the colony.

7. A soap company interviewed 800 people in a city. It was found out that $\frac{3}{8}$ use brand A soap, $\frac{1}{5}$use brand B soap, 70 use brand A and B soap, 55 use brand B and C soap, 60 use brand A and C soap and $\frac{1}{40}$ use all the three brands Find,
(i) Number of people who use exactly two branded soaps,
(ii) Number of people who use atleast one branded soap,
(iii) Number of people who do not use any one of these brands.

8. A survey of 1000 farmers found that 600 grew paddy, 350 grew ragi, 280 grew corn, 120 grew paddy and ragi, 100 grew ragi and corn, 80 grew paddy and corn. If each farmer grew atleast any one of the above three, then find the number of farmers who grew all the three.

9. Each student in a class of 35 plays atleast one game among chess, carrom and table tennis. 22 play chess, 21 play carrom, 15 play table tennis, 10 play chess and table tennis, 8 play carrom and table tennis and 6 play all the three games. Find the number of students who play (i) chess and carrom but not table tennis (ii) only chess (iii) only carrom.

10. A survey was conducted among 200 magazine subscribers of three different magazines A, B and C. It was found that 75 members do not subscribe magazine A, 100 members do not subscribe magazine B, 50 members do not subscribe magazine C and 125 subscribe atleast two of the three magazines. Find
(i) Number of members who subscribe exactly two magazines.
(ii) Number of members who subscribe only one magazine