92. (Sets) By T.KallayaneeNupad
37.
1. 2.
3. 4.
38.
1. 2.
3. 4. U
39.
40.
93. (Sets) By T.KallayaneeNupad
41.
42. U
1. 2.
3. 4.
43. U
1. 2.
3. 4.
44. U
1. 2.
94. (Sets) By T.KallayaneeNupad
3. 4.
45. U
1. 2.
3. 4.
46. U
1. 2.
3. 4.
47.
1. 2. U 3. 4.
48.
1. 2. U 3. 4.
49.
1. 2. U 3. 4.
50.
1. 2.
3. 4.
95. (Sets) By T.KallayaneeNupad
4
4.1
A= 0,2,3,5,7 A 5
B= 4, 1.2.6 B 4
C= C 0
A 5
1
A, B, C , A B, B C, B , C A, B C ' , A C
96. (Sets) By T.KallayaneeNupad
U= 2, 1,0,2,4,5,8
A= 2,0,4,8
B= 1,0,2
C= 2,2,5
nA 4, n B 3,n C 3
A B 0 nA B 1
B C 2, 1,0,2,5 nB C 5
B 2,4,5,8 nB 4
C A 2,5 nC A 2
B C 1,0
'
B C 2,2,4,5,8 n B C 5
A 1,2,5
A C 2,5 nA C 2
2 A B C, A B C, A B C
A B C
U= x I 3 x 3
A= x x3 2 x 2 3x 0
B= x x 2 6x 9 0
C= x x2 1
U= 3, 2, 1,0,1,2,3
A= x x3 2 x 2 3x 0
97. (Sets) By T.KallayaneeNupad
x3 2 x 2 3x 0
2
xx 2x 3 0
xx 3 x 1 0
A= 3,0,1
B= x x 2 6x 9 0
x2 6x 9 0
2
x 3 0
x 3 0
x 3
B= 3
C= x x2 1
x2 1
x2 1 0
x 1 x 1 0
C= 1,1
A B C nA B C 0
A B C 3, 1,0,1 nA B C 4
A B C 3, 2, 1,0,1,2,3 n A B C 7
A B C 2,2,3 n A B C 3
98. (Sets) By T.KallayaneeNupad
1. A B
- A B
nA B nA nB
- A B
nA B nA nB nA B
2. A B C
nA B C nA nB nC nA B nB C nA C nA B C
99. (Sets) By T.KallayaneeNupad
3. A–B
nA B nA nA B
4. B–A
nB A nB nA B
5. A
nA nU nA
–
nA 3 2 5
nB 2 1 3
nA B 2
100. (Sets) By T.KallayaneeNupad
nA 2 1 1 0 4
nB 3 1 1 2 7
nC 5 0 1 2 8
n A B 1 1 2
nB C 1 2 3
n A C 1 0 1
n A B C 1
3 10, n A 3, n B 4, n A B 1
n A ,n B ,n A B ,n B A ,n A B
n A nU n A 10 3 7
n B nU n B 10 4 6
n A B n A n A B 3 1 2
n B A nB n A B 4 1 3
n A B n A nB n A B 3 4 1 6
4 A B A B 7 A
3
B 4
nA B nA nB nA B
7 3 4 nA B
nA B 0
101. (Sets) By T.KallayaneeNupad
A B 0
5A B C nA 8, n B 6, n C 10,
nA B nA C nB C 3, n A B C 1
nA B C nA nB nC nA B nB C nA C nA B C
8 6 10 3 3 3 1
16
A B C 16
6A – B nA 7 ,n B 4 ,n A B 8
- nA B
nA B nA nB nA B
8 7 4 nA B
nA B 3
- n A B
nA B nA nA B
7 3
4
A B 4
102. (Sets) By T.KallayaneeNupad
4.1
1. 2,3,5,7,810 , A 2,7,10 , B 3,5,7,8
1.1 A 1.2 B
1.3 A 1.4 B
1.5 A B 1.6 B A
103. (Sets) By T.KallayaneeNupad
1.7 A B 1.8 B A
1.9 A B 1.10 B A
2. 3, 1,0,2,4,5,9 , A 3,0,2,9 , B 1,0,4,9 , C 0,2,4,9
2.1 A B 2.2 C B
2.3 A B 2.4 B C
2.5 B A 2.6 B C
2.7 A B C 2.8 A B C
104. (Sets) By T.KallayaneeNupad
2.9 A B C 2.10 B A C
3. x 4 x 4
A x x3 5x 2 8x 48 0
B x x3 4 x 2 9 x 36 0
C x I x3 9 x 2 24x 16 0
3.1 A 3.2 B
3.3 C 3.4 U
3.5 A B 3.6 B C
3.7 C B 3.8 B
105. (Sets) By T.KallayaneeNupad
3.9 B C 3.10 A C
3.11 B A C 3.12 C A B
4. U 10, n A 7, n B 3, n A B 2
4.1 A 4.2 B
4.3 A B 4.4 B A
4.5 A B 4.6 A B
4.7 A B 4.8 B A
4.9 A B
106. (Sets) By T.KallayaneeNupad
5. U 20 , n A 8, n B 8, n C 7, n A B 3, n B C 3,
nA C 4, n A B C 2
5.1 A 5.2 B
5.3 C 5.4 A B
5.5 B C 5.6 B A
5.7 A C 5.8 C A
5.9 A B C 5.10 B C A
5.11 A B C 5.12 A B C
107. (Sets) By T.KallayaneeNupad
6. A B nA 4, n B 5 A B
7. A B nA 3, n B 7, n A B 1
8. nA 5, n B 3, n A B 2
8.1 A B
8.2 B A
108. (Sets) By T.KallayaneeNupad
9. nA 12, n B 9, U 15
9.1 A
9.2 B
10. A B C nA 7, n B 4, n C 7, n A B 2,
nB C 3, n A C 4, n A B C 2
11. A B nA 9, n B 7, n C 6, n A B 2,
nB C 3, n A C 3, n A B C 1, n A B C 15
109. (Sets) By T.KallayaneeNupad
12. nA B 2 nA B 12 nA nB A B
13. nA B 1 nA B 9 A
B
2 A B
14. A B n A B 1
nB A 2
nA B 8 n A B
15. n A 8, n B 8, n C 6, n A B 3, n( B C ) 3, n( A C) 4, n( A B C ) 14
15.1 A B C 15.2 A B
110. (Sets) By T.KallayaneeNupad
15.3 B C 15.4 B'
15.5 B C' 15.6 A' B
15.7 A B C 15.8 B (A C)
16. U 20, n( A B C )' 4, n( A B) n( A B C) 1
n( B C) n( A B C) 1 , n( A C ) n( A B C)
3
n( A) 8, n( B) 8, n(C ) 9 B'
111. (Sets) By T.KallayaneeNupad
4.2
-
7 10 8
7
1
-
A
B
A B
A B
113. (Sets) By T.KallayaneeNupad
n( A B) n( A) n( B) n( A B)
10 8 7 n( A B)
10 15 n( A B)
n( A B) 5
5
8 14 4
7 4
4
4 1
4
A 4
B 4
A B
A B 4
n( A B) n( A) n( B) n( A B)
114. (Sets) By T.KallayaneeNupad
14 7 4 x
14 11 x
x 3
4 3
9 10
1
3 4
U
A
B
A B
A B
(A B)'
-
n( A B)' n( ) n( A B)
1 10 n( A B)
n( A B) 9
-
n( A B) n( A) n( B) n( A B)
115. (Sets) By T.KallayaneeNupad
9 ( x 3) ( x 4) x
9 x 7
x 2
3 x 3 2 5
10 3
11
4
A
B
A B
A B
n(B) x 3
n(A) x 7
n( A B) n( A) n( B) n( A B)
11 ( x 7) ( x 3) 3
11 2 x 7
2x 4
x 2
x 3 2 3 5
11 11 9
6
116. (Sets) By T.KallayaneeNupad
4 2
3
1
A
B
C
5 4 2 11
12 68
7 5
9
3
2
5
55
A
117. (Sets) By T.KallayaneeNupad
B
C
A B
B C
A C
A B C
A B C 1
(A B C )'
n( A B C )' n( ) n( A B C)
55 68 n( A B C)
n( A B C ) 13
n( A B C ) n( A) n( B) n(C ) n( A B ) n( B C ) n( A C ) n( A B C)
13 7 5 9 3 2 5 x
13 11 x
x 2
1
137. (Sets) By T.KallayaneeNupad
1.6
1.7
1.8 2 9
2. 2.1 -1,0,1 A -1,0,1
U
2.2 -1,0,1 B 0,1
U 0
2.3 0 C
U
2.4 0 D
U
2.5 E -3,5
U
2.6 F -3
U
2.7 G
U
2.8 0 x 2H
U
140. (Sets) By T.KallayaneeNupad
1.9 1.10
1.11 1.12
2. 2.1U 4, 3, 2, 1,0,1,2,3,4,5,6 2.2 U 2, 1,0,1,2,3,4,5
A 1,6 A 5
B 4,4 B 3,5
2.3 U 3, 2, 1,0,1,2,3,4,5 2.4 U 2, 1,0,1,2,3,4,5
A 3,2 A 5
B 2,5 B 2,2,5
2.5 U 1,2,3,4,5 2.6 U 1,2,3,4,5
141. (Sets) By T.KallayaneeNupad
A 2,4 A 1,2,5
B 3,4 B 3
C 1,4 C 1,3
2
1. 1 2. 4 3.3 4.3 5.2 6.4 7.1 8.1 9. 2
10. 4 11. 4 12.1 13.4 14.2 15.3 16.1 17.3 18. 3
19. 4 20. 4 21.4 22.2 23.3 24.2 25.3 26.4 27. 2
28. 4 29. 1 30. 2
3
3.1
1. 1.1 1.2
1.3 1.4
1.5 1.6
143. (Sets) By T.KallayaneeNupad
4.3 4.4
4.5 4.6
5. A B 1,2,5,6,9
A B B
B A B
A B A B B
6. A 2, 1,0,1,2
B 1,2
A B 2, 1,0,1,2
A B A
A A B
B A A B A
3.2
1. 1.1 1.2
145. (Sets) By T.KallayaneeNupad
5. 5.1 5.2
5.3 5.4
5.5 5.6
5.7 5.8
6. 6.1 A 3,1,2 6.2 A 5,5
146. (Sets) By T.KallayaneeNupad
B 3,5 B 3
A B 3 A B
6.3 A 3, 1,13 6.4 A 2,4,6,8,...
B 1,3 B 2,4,6
A B 1,3 A B 2,4,6
7. A B 3,1,6,9
A B A
A
A B
A B A B A
8. A 6,5,6
B 6,1
C 6, 2,2
B C 6, 2,1,2
A (B C) 6
A B 6
A C 6
( A B) (A C) 6
A (B C) ( A B) ( A C)
3.3
1. 1.1 1.2
1.3 1.4
1.5 1.6
1.7 1.8
2. 2.1 2.2
148. (Sets) By T.KallayaneeNupad
5. 5.1 5.2
5.3 5.4
5.5 5.6
5.7 5.8
6. 6.1 A 1,3 6.2 A 5,5
B 3, 4 B 4,2
A B 1 A B 5,5
6.3 A 7, 5,5,7 6.4 A 5,10 ,15,20 ,...
B 5 B 5,15
149. (Sets) By T.KallayaneeNupad
A B 7,5,7 A B 10,20,25,30,...
7. B C 0,2,5,7,8,9
A (B C) 6
A B 0,6
A C 2,6
( A B) ( A C ) 6
A ( B C ) ( A B) ( A C)
8. A B 8
(A B) C 8
A C 5,7,8
B C 0,1,8
( A C) (B C) 8
( A B) C ( A C ) (B C)
9. A 2, 1,0,1,2
B 2
C 1,3
A B) 2, 1,0,1,2
( A B) C 2, 1,0,2
A C 2, 1,0,2
B C 2
( A C) (B C) 2, 1,0,2
( A B) C ( A C ) ( B C )
3.4
1. 1.1 1.2
1.3 1.4
1.5 U 1.6 U
2. 2.1 2.2
2.3 2.4
151. (Sets) By T.KallayaneeNupad
3.9 3.10
4. 4.1 U= 0,1,2,3,4,5,6,7,8 4.2 U= 5,10 ,15,20 ,...
A 1,2,5 A 10 ,15
A' 0,3,4,6,7,8 A' 5,20 ,25,30 ,...
4.3 U= 4, 3, 2, 1,0,1,2,3,4
A 2,2
B 3,3
A B 3, 2,2,3
( A B)' 4, 1,0,1,4
4.4 U= 2, 1,0,1,2,3,4,5.
A 1,0,3
B 2,4
A' 2,1,2,4,5
B' 1,0,1,2,3,5
A' B ' 1,2,5
5. A' 3,4,9
A A'
6. A B
(A B )' 4, 2,1,3,5,6,9
A' 2,5,6,9
B' 4, 2,1,3,5,6,9
A' B ' 4, 2,1,3,5,6,9
( A B )' A' B '
152. (Sets) By T.KallayaneeNupad
7. U= 5, 4, 3, 2, 1,0,1,2,3
A 3,1
B 5, 3,3
A B 5, 3,1,3
(A B )' 4, 2, 1,0,2
A' 5, 4, 2, 1,0,2,3
B' 4, 2, 1,0,1,2
A' B ' 4, 2, 1,0,2
( A B )' A' B '
3
1. 1 2. 3 3.4 4.2 5.4 6.1 7.3 8.1 9. 1
10. 3 11. 4 12.1 13.2 14.4 15.4 16.2 17.1 18. 4
19. 3 20. 2 21.2 22.1 23.2 24.2 25.2 26.2 27. 2
28. 4 29. 1 30.4 31.2 32.1 33.3 34.2 35.3 36. 3
37. 2 38. 4 39.4 40.2 41.1 42.2 43.4 44.1 45. 1
46. 4 47. 1 48.2 49.3 50. 3
154. (Sets) By T.KallayaneeNupad
1. 1.1 n(A) 3 1.2 n(B) 4
1.3 A' 3,5,8 1.4 B' 2,10
n(A' ) 3 n(B' ) 2
1.5 A B 7 1.6 B A 2,3,5,7,8,10
n( A B) 1 n( B A) 6
1.7 A B 2,10 1.8 B A 3,5,8
n( A B) 2 n( B A) 3
1.9 A B 2,3,5,7,8,10 1.10 B' 2,10
(A B)' B' A 2,10
n(( A B)') 0 n( B' A) 2
2. 2.1 A B 3, 1,0,2,4,9 2.2 C B 0,4,9
n( A B) 6 n(C B) 3
2.3 A B 3,2 2.4 B C 1
n( A B) 2 n( B C ) 1
2.5 B A 1,4 2.6 B C 1,0,2,4,9
(B A)' 3,0,2,5,9 (B C )' 3,5
n((B A)') 5 n((B C )') 2
2.7 A B C 3, 1,0,2,4,9 2.8 A B C 0,9
n( A B C) 6 n( A B C) 2
2.9 B C 1 2.10 B A 0,9
A (B C) 3,0,2,9 (B A) C 0,2,4,9
n( A ( B C )) 4 n((B A) C) 4
3. U= 4, 3, 2, 1,0,1,2,3,4
155. (Sets) By T.KallayaneeNupad
A 3,4
B 4, 3,3
C 1,4
3.1 n(A) 2 3.2 n(B) 3
3.3 n(C ) 2 3.4 n( U ) 9
3.5 A B 4, 3,3,4 3.6 B C
n( A B) 4 n( B C) 0
3.7 C B 1,4 3.8 B' 2, 1,0,1,2,4
n(C B) 2 n(B' ) 6
3.9 B C 4, 3,3 3.10 A C 3,1,4
( B C )' 2, 1,0,1,2,4 (A C )' 3,1,4
n((B C )') 6 n(( A C )') 3
3.11 B A 3 3.12 C A 3,1,4
(B A) C 3 (C A) B 3
n((B A) C ) 1 n((C A) B) 1
4.
4.1 n(A' ) 3 4.2 n(B' ) 7
4.3 n( A B) 5 4.4 n( B A) 1
4.5 n( A B) 8 4.6 n( A B)' 2
4.7 n( A B)' 5 4.8 n( B A)' 9
4.9 n( A B)' 8
156. (Sets) By T.KallayaneeNupad
5.
5.1 n(A' ) 12 5.2 n(B' ) 12
5.3 n(C ' ) 13 5.4 n( A B) 13
5.5 n( B C) 3 5.6 n( B A) 5
5.7 n( A C )' 16 5.8 n(C A)' 17
5.9 n(( A B) C) 5 5.10 n( B (C A)) 4
5.11 n( A B C ) 15 5.12 n( A B C )' 5
6. n( A B) n( A) n( B) 4 5 9
7. n( A B) n( A) n( B) n( A B) 3 7 1 9
8. 8.1 n( A B) n( A) n( A B) 5 2 3
8.2 n( B A) n( B) n( A B) 3 2 1
9. 9.1 n( A' ) n( U ) n( A) 15 12 3
9.2 n( B ' ) n( U ) n( B) 15 9 6
10. n( A B C ) n( A) n( B) n(C ) n( A B) n( B C ) n( A C ) n( A B C)
7 4 7 2 3 4 2 11
11. n( A B C ) n( A) n( B) n(C ) n( A B) n( B C ) n( A C ) n( A B C)
157. (Sets) By T.KallayaneeNupad
15 9 7 6 n( A B) 3 3 1
15 17 n( A B )
n( A B) 2
12.
n( A B) 5
13. n(A) 6 n(B) 4
14. n( A B) 5
15. n( A B C ) n( A) n( B) n(C ) n( A B) n( B C ) n( A C ) n( A B C)
14 8 8 6 3 3 4 x
14 12 x
x 2
15.1 n( A B C) 2 15.2 n( A B) 13
15.3 n( B C ) 5 15.4 n(B' ) 6
15.5 n( B C )' 3 15.6 n( A' B) 1
15.7 n(( A B) C ) 8 15.8 n( B ( A C )) 6
16. - n( A B C)
n( A B C )' n( ) n( A B C)
4 20 n( A B C)
n( A B C ) 16
158. (Sets) By T.KallayaneeNupad
- n( A B C)
n( A B C) x
n( A B C) n( A) n( B) n(C ) n( A B ) n( B C ) n( A C ) n( A B C)
16 8 8 9 ( x 1) ( x 1) ( x 3) x
16 20 2 x
2x 4
x 2
- B'
n( B ' ) n( ) n( B) 20 8 12
B' 12
4.2
1. 3
2. 8
3. 3
4. 5
5.
6. 5
7. 7
8. 13
9. 40
10. 2