Question 1 [13 marks] a) Consider the following sets: A.(1, 3, 5, 7, 9, B, D, F}

Question

Question 1 [13 marks] a) Consider the following sets: A.(1, 3, 5, 7, 9, B, D, F},B+{0, 3, 6, 9, C,FJ and C. {0, 2, 4, 6, 8, A, C,E), which are constructed from the Universal set-0,1,2,3, 4,5,6,7,8,9, A, B, C, D, E, F. Set D which is defined from the same Universal set is represented by the following bit pattern: 0000000000111111 Write down the elements of set D Using the bit pattern representation and bit operations, find the bit pattern that represents the following sets. Use a Venn diagram to verify your answer. i) Au B i) AuC iii) A B iv) BnC b) Consider the sets Prod Name P Apples, Pears, Peaches, Oranges)and Buyer_ID B (0, 1,2,3. Find the following: The Cartesian product, Px B. i) P2 iti) How many subsets of B can be constructed. List all the possible subsets of B.

Explanation / Answer

Hi,

a)

i)

D={0,2,F}

ii)

i) AUB={0,1,2,3,5,7,8,9,B,D,F}

00000001001000110101011110001001101111011111

ii)^AUC={0,2,4,6,8,A,C,E}

00000011010001101000101011001110

iii) A-B={1,5,7,B,D}

00010101011110111101

iv) = {0,6,C}

000001101100

b)

i)

{(Appless, 0),(Apples,1),(Apples,2),(Apples,3), (Pears, 0),(Pears,1),(Pears,2),(Pears,3), (Peaches, 0),(Peaches,1),(Peaches,2),(Peaches,3), (Oranges, 0),(Oranges,1),(Oranges,2),(Oranges,3)}

ii)

{(Appless, Appless),(Apples,Pears),(Apples,Peaches),(Apples,Oranges), (Pears, Apples),(Pears,Pears),(Pears,Peaches),(Pears,Oranges), (Peaches, Apples),(Peaches,Pears),(Peaches,Peaches),(Peaches,Oranges), (Oranges, Apples),(Oranges,Pears),(Oranges,Peaches),(Oranges,Oranges)}

iii)

B={0,1,2,3}

number of subsets=2^4=16

Subset = {},{0},{1},{2},{3},{0,1}{0,2},{0,3},{2,1},{2,3},{3,1},{0,1,2},{1,2,3},{0,1,3},{2,3,0},{0,1,2,3}

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