47. Let A¡ = {1, 2, 3, . . , i} for i = 1, 2, 3, .... Find %3D %3D UA. b) Aj. a) i=1

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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41. Suppose that A, B, and C are sets such that A C =
BOC.Must it be the case that A = B?
%3D
42. If A, B, C, and D are sets, does it follow that (A B)
(C D) = (A C) ® (B D)?
43. If A, B, C, and D are sets, does it follow that (A B) Ð
(C D) = (A O D) & (B Ð C)?
44. Show that if A and B are finite sets, then A U B is a finite
set.
45. Show that if A is an infinite set, then whenever B is a set,
AUB is also an infinite set.
* 46. Show that if A, B, and C are sets, then
JAUBUC= |A|+|B|+ |C| – |AO B|
- |ANC| – |B NCl+ |AN BN CI.
(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
a) UA,.
b) 4i.
i=1
i-1
48. Let A, = (...,-2,-1,0, 1, ..., i}. Find
a) U
b) Ai.
Transcribed Image Text:41. Suppose that A, B, and C are sets such that A C = BOC.Must it be the case that A = B? %3D 42. If A, B, C, and D are sets, does it follow that (A B) (C D) = (A C) ® (B D)? 43. If A, B, C, and D are sets, does it follow that (A B) Ð (C D) = (A O D) & (B Ð C)? 44. Show that if A and B are finite sets, then A U B is a finite set. 45. Show that if A is an infinite set, then whenever B is a set, AUB is also an infinite set. * 46. Show that if A, B, and C are sets, then JAUBUC= |A|+|B|+ |C| – |AO B| - |ANC| – |B NCl+ |AN BN CI. (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 a) UA,. b) 4i. i=1 i-1 48. Let A, = (...,-2,-1,0, 1, ..., i}. Find a) U b) Ai.
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