a) Consider the following sets:

?? = {1, 3, 5, 7, 9, ??, ??, ??}, ?? = {0, 3, 6, 9, ??, ??} and ?? = {0, 2, 4, 6, 8, ??, ??, ??},

which are constructed from the Universal set?? = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, ??, ??, ??, ??, ??, ??}.

i) Set ?? which is defined from the same Universal set ?? is represented by the following bit pattern:

0000000000111111.

Write down the elements of set ??.

ii) 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) ?? ? ??

ii) ?? ? ??

iii) ?? ? ??

iv) ?? ? ?? b)

Consider the sets Prod_Name = ?? = {Apples, Pears, Peaches, Oranges} and Buyer_ID = ?? = {0, 1, 2, 3}. Find the following:

i) The Cartesian product, ?? ??.

ii) ?? 2

iii) How many subsets of ?? can be constructed. List all the possible subsets of ??.