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please send handwritten solution for Q3 part 1

please send handwritten solution for Q3 part 1

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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please send handwritten solution for Q3 part 1
3. Sets 1. Let A = {1, 2, 3, 4, 5} and B = {1,2,3, 4, 5, 6}. Give a set T C AO B so that following three constraints are all satisfied: (a) Va E A 3b E B: (a, b) ET, (b) VE В За € А: (а, b) € Т, and (c) |T| is as small as possible. What is the size |T| as a function of |A| and |B|? Justify your answers. 2. Let A1 = {0} and B1 = {1}. For n> 1, recursively define An = (An-1 ® {0}) U (Bn-1 8 {1}) B, = (An-1® {1}) U (B-18 {0}). (a) List the elements in A3 in lexicographical order, and list the elements in B3 in lexico- graphical order. Justify. (b) Give a characterization of the elements in A, for arbitrary n 2 1 in plain English. Еxplain.
Transcribed Image Text:3. Sets 1. Let A = {1, 2, 3, 4, 5} and B = {1,2,3, 4, 5, 6}. Give a set T C AO B so that following three constraints are all satisfied: (a) Va E A 3b E B: (a, b) ET, (b) VE В За € А: (а, b) € Т, and (c) |T| is as small as possible. What is the size |T| as a function of |A| and |B|? Justify your answers. 2. Let A1 = {0} and B1 = {1}. For n> 1, recursively define An = (An-1 ® {0}) U (Bn-1 8 {1}) B, = (An-1® {1}) U (B-18 {0}). (a) List the elements in A3 in lexicographical order, and list the elements in B3 in lexico- graphical order. Justify. (b) Give a characterization of the elements in A, for arbitrary n 2 1 in plain English. Еxplain.
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