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(a) For A = {1, 2, 3}, give an example of three subsets A1,A2 and A3 of A such that

Chapter 2, Problem 26

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QUESTION:

(a) For A = {1, 2, 3}, give an example of three subsets A1,A2 and A3 of A such that |AiAj | =|i j| for every pair i, j of distinct integers with 1 i, j 3.(b) For B = {1, 2, 3, 4, 5, 6}, give an example of four subsets B1,B2, B3 and B4 of B suchthat |Bi Bj | = |i j| for every pair i, j of distinct integers with 1 i, j 4.2

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QUESTION:

(a) For A = {1, 2, 3}, give an example of three subsets A1,A2 and A3 of A such that |AiAj | =|i j| for every pair i, j of distinct integers with 1 i, j 3.(b) For B = {1, 2, 3, 4, 5, 6}, give an example of four subsets B1,B2, B3 and B4 of B suchthat |Bi Bj | = |i j| for every pair i, j of distinct integers with 1 i, j 4.2

ANSWER:

Problem 26

(a) For , give an example of three subsets ,  and  of  such that   for every pair  of distinct integers with .

(b) For , give an example of four subsets , ,  and  of such that  for every pair  of distinct integers with .

                                                               Step By Step Solutions

Step 1 of 3

Here the condition is  for every pair  of distinct integers with . That is,  is the set of all elements that belong to both the set  and and  means the number of elements in  should be equal to for every pair  of distinct integers with . .

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