#### Set Language Model Questions

9th Standard

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Maths

Time : 01:00:00 Hrs
Total Marks : 50
5 x 1 = 5
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. If J = Set of three sided shapes, K = Set of shapes with two equal sides and L = Set of shapes with right angle, then J ∩ K ⋂ L is

(a)

Set of isoceles triangles

(b)

Set of equilateral triangles

(c)

Set of isoceles right triangles

(d)

Set of right angled triangles

3. 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)

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

4. $\left( A\cup B\cup C \right) \cup \left( A\cup BC \right) ^{ ' }$=_______

(a)

$\Phi$

(b)

A

(c)

U

(d)

$A\cap B\cap C$

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

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

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

8. 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.

9. If A={ x : x = 2n, n $\in$ W and n<4}, B = {x : x = n, n  2 $\in$ N and n ≤ 4} and C = {0, 1, 2, 5, 6} , then verify the associative property of intersection of sets.

10. 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 $A\cup (B\cap C)=(A\cup B)\cap (A\cup C)$.

11. State Associative property of sets.

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

13. 6 x 3 = 18
14. If K = {a,b,d e f }  L = {b,c,d,g} and M = {a,b,c,d,h}, then find the following:
(i) K $\cup$(L $\cap$ M)
(ii) K $\cap$(L $\cup$ M)
(iii) (K$\cup$L)$\cap$(K$\cup$M)
(iv)
(K$\cap$L)$\cup$(K$\cap$M)

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

16. In the adjacent diagram, if n(U) = 125, y is two times of x and z is 10 more than x, then find the value of x,y and z.

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

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

19. Verify A -(BUC) = (A-B)∩(A-C) using Venn diagrams.

20. 3 x 5 = 15
21. 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)

22. If U = {x :x $\in$  Z, -3 $\le$ x $\le$ 9 },A = {x : x = 2P +1, $\in$ Z, -2 $\le$ P$\le$ 3}, B ={x : x = q + 1, q $\in$ Z, 0 $\le$ q $\le$ 3}, verify De Morgan's law's for complementation.

23. If A = {b, c, d, e} and B = {b, c, e, g} and C= {a, c, e}, then verify $A\cup \left( B\cup C \right)$ = $\left( A\cup B \right) \cup C$