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b. Suppose the universal set is .i. Write in enumerated form the set that is represented by the bit string .ii. If is represented the bit string and is represented by the bit string , write the sets AUB and A as bit strings.
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Q. b. Suppose the universal set is .i. Write in enumerated form the set that is represented by the bit string .ii. If is represented the bit string and is represented by the bit string , write the sets AUB and A as bit strings.
- Convert to Set: To solve the first part of the problem, we need to convert the bit string into a set by matching each bit to the corresponding element in the universal set . A '' in the bit string means the element is included in the set, while a '' means it is not included.
- Enumerate Set: Enumerate the set represented by the bit string . Starting from the left, the first bit is , so is not included. The second bit is , so is included, and so on. The resulting set is \{\}.
- Find Union: To solve the second part of the problem, we need to find the union of sets and , represented by their respective bit strings. The union of two sets includes all elements that are in either set. In terms of bit strings, we perform a logical operation on each pair of corresponding bits.
- Perform OR Operation: Perform the logical OR operation on the bit strings for () and (). The result is , as each pair of bits has at least one '' except for the last pair.
- Resulting Set: The set represented by the bit string is \{,,,,,,,\}, as all bits except the last one are ''.
- Given Set: The set is already given by the bit string , so no further calculation is needed for this part.
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