48. Let A, = {...,-2, –1,0, 1, ...,i). Find %3D a) Aj. b)4-

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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(C D) = (A OC) (B BY?
43. If A, B, C, and D are sets, does it follow that (A B)
(C D) = (A D) (B O C)?
c)
54. What
repre
%3D
a) t
44. Show that if A and B are finite sets, then A UB is a finite
b) t
55. Wh.
set.
45. Show that if A is an infinite set, then whenever B is a set,
AUB is also an infinite set.
twc
56. WE
fer
46. Show that if A, B, and C are sets, then
57. SE
JAUBUC=|A|+ |B|+ \C| - 1AN B|
- |ANC| – |BOCl + |AN BOC).
us
(This is a special case of the inclusion-exclusion princi-
ple, which will be studied in Chapter 8.)
47. Let A; = (1, 2, 3, .., i} for i = 1, 2, 3, . . Find
%3D
%3D
*...
58.
b) ÑA.
a)
Aj.
Ai.
i=1
The
48. Let A; = {..., -2, –1,0, 1, .,i}. Find
%3D
59.
a)
Aj
b) N4-
Aj-
-
Transcribed Image Text:(C D) = (A OC) (B BY? 43. If A, B, C, and D are sets, does it follow that (A B) (C D) = (A D) (B O C)? c) 54. What repre %3D a) t 44. Show that if A and B are finite sets, then A UB is a finite b) t 55. Wh. set. 45. Show that if A is an infinite set, then whenever B is a set, AUB is also an infinite set. twc 56. WE fer 46. Show that if A, B, and C are sets, then 57. SE JAUBUC=|A|+ |B|+ \C| - 1AN B| - |ANC| – |BOCl + |AN BOC). us (This is a special case of the inclusion-exclusion princi- ple, which will be studied in Chapter 8.) 47. Let A; = (1, 2, 3, .., i} for i = 1, 2, 3, . . Find %3D %3D *... 58. b) ÑA. a) Aj. Ai. i=1 The 48. Let A; = {..., -2, –1,0, 1, .,i}. Find %3D 59. a) Aj b) N4- Aj- -
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