#### Set Language Book Back Questions

9th Standard

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Maths

Time : 00:45:00 Hrs
Total Marks : 30
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. 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 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

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. In a city, 40% people like only one fruit, 35% people like only two fruits, 20% people like all the three fruits. How many percentage of people do not like any one of the above three fruits?

(a)

5

(b)

8

(c)

10

(d)

15

6. 3 x 2 = 6
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. 3 x 3 = 9
11. If A={b,e,f,g} and B={c,e,g,h}, then verify the commutative property of (i) union of sets (ii) intersection of sets.

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

13. If A = {b,c,e,g,h} , B = {a,c,d,g,i} and C = {a,d,e,g,h} , then show that $A-(B\cap C)=(A-B)\cup (A-c)$.

14. 2 x 5 = 10
15. 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

16. 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.