#### Set Language Model Question Paper

9th Standard

Reg.No. :
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Maths

Time : 01:30:00 Hrs
Total Marks : 50
7 x 1 = 7
1. If U={x:x$\in$N and x<10}, A={1, 2, 3, 5, 8} and B={2, 5, 6, 7, 9}, then $n\{ (A\cup B)'\}$ is

(a)

1

(b)

2

(c)

4

(d)

8

2. Which of the following is true?

(a)

A-B=A$\cap$B

(b)

A−B = B −A

(c)

(A$\cup$B)'=A'$\cup$B'

(d)

(A$\cap$B)'=A'$\cup$B'

3. If n(A U B U C) = 100, n(A) = 4x, n(B) = 6x, n(C) = 5x, n(A ∩ B) = 20, n(B ⋂C) = 15, n(A C) = 25 and n(A ⋂ B ⋂ C) = 10 , then the value of x is

(a)

10

(b)

15

(c)

25

(d)

30

4. If A and B are two non-empty sets, then (A-B)U(A⋂B) is

(a)

A

(b)

B

(c)

ф

(d)

U

5. For any three A,B and C,$A-\left( B\cup C \right)$

(a)

(A-B)$\cup$(A-C)

(b)

(A-B)$\cap$(A$\cup$C)

(c)

(A-B)$\cup$C

(d)

A$\cup$(B-C)

6. If A,B,C are non-overlapping sets,then n $\left( A\cap B\cap C \right)$ is ___________

(a)

n(A) + n(B) + n(C)

(b)

$n\left( A\cup B\cup C \right)$

(c)

0

(d)

$n\left( A\cap B \right)$

7. $n(A\cup B\cup C)$=________

(a)

n(A) + n(B) + n(C)

(b)

n(A) + n(b) + n(C) -$n\left( A\cap B\cap C \right)$

(c)

$n\left( A\cap B\cap C \right)$

(d)

n(A) + n(B) + n(C) -$n\left( A\cap B \right)$-$n\left( B\cap A \right) -n\left( A\cap C \right) +n\left( A\cap B\cap C \right)$

8. 6 x 2 = 12
9. If A = {2, 3, 4, 5}, B = {2, 3, 5, 7} and C = {1, 3, 5}, then verify $A\cup (B\cup C)=(A\cup B)\cup C$.

10. If P = {1,2,5,7,9}, Q = {2, 3, 5, 9, 11}, R = {3, 4,5 7, 9} and S = {2, 3, 4, 5, 8}, then find
(i) $(P\cup Q)\cup R$
(ii) $(P\cap Q)\cap S$
(iii) $(Q\cap S)\cap R$

11. If A = {p,q,r,s}, B = {m,n,q,s,t} and C = {m,n,p,q,s}, then verify the associative property of union of sets.

12. If A = {0, 2, 4, 6, 8},B ={x : x is a prime number and x < 11} and C={x:x$\in$N and 5 ≤ x < 9} then verify $A\cup (B\cap C)=(A\cup B)\cap (A\cup C)$.

13. State Associative property of sets.

14. State the formula to find $n\left( A\cup B\cup C \right)$

15. 7 x 3 = 21
16. Verify $A\cap (B\cup C)=(A\cap B)\cup (A\cap C)$ using Venn diagrams.

17. If A={11,13,14,15,16,18}, B={11,12,15,16,17,19}, and C={13,15,16,17,18,20}, then verify $A\cap (B\cup C)=(A\cap B)\cup (A\cap C)$.

18. Verify $A-(B\cap C)=(A-B)\cup (A-C)$using Venn diagrams.

19. Verify $(A\cap B)'=A'\cup B'$ using Venn diagrams.

20. P = {x : x$\in$W and 0 < x < 10} Q = {x : x = 2n+1, n$\in$W and n < 5} and R = {2, 3, 5, 7, 11, 13  then verify P −(Q ⋂ R) = (P − Q) U (P −R).

21. If A={-2,0,1,3,5}, B={-1,0,2,5,6} and C={-1,2,5,6,7} then show that A-(BUC)=(A-B)∩(A-C).

22. If A={2,5,6,7} and B={3,5,7,8}, then verify the commulative property of : union sets

23. 2 x 5 = 10
24. 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 $A-(B\cap C)=(A-B)\cup (A-C)$.

25. 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.