please send handwritten solution for Q3 part 1
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 87E
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F44338f17-69d2-496e-9275-0093ae5f472a%2Ff603795a-4003-4298-a945-6c066ae40748%2Fmg5tx8k_processed.jpeg&w=3840&q=75)
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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