Final answer:
The power set of T = {0, 1, 2, 3} includes the empty set and all combinations of elements in T. The options provided do not accurately represent the power set of T. Option C is the closest as it contains the empty set and the set itself, but it does not list all subsets.
Step-by-step explanation:
The power set of a set is the set of all subsets of that set, including the empty set and the set itself. If we have a set T and we're looking for the power set of 2T - 2, we first need to determine what 2T represents. In this context, because no operation is explicitly defined for 'multiplying' a set by an integer or subtracting an integer from a set, the expression '2T - 2' would not normally have meaning in set theory. However, treating the question as if it may contain a typo or mistake, we will deduce that we are likely asked to find the power set of T and then simply present it in the question's erroneous format.
The set T = {0, 1, 2, 3}. The power set of T, denoted as P(T), includes the empty set and all possible combinations of the elements of T. Therefore, the power set of T is:
- {} (the empty set)
- {0}
- {1}
- {2}
- {3}
- {0, 1}
- {0, 2}
- {0, 3}
- {1, 2}
- {1, 3}
- {2, 3}
- {0, 1, 2}
- {0, 1, 3}
- {0, 2, 3}
- {1, 2, 3}
- {0, 1, 2, 3}
From the multiple-choice options provided, none directly describe the power set of T. If we ignore typos and irrelevant parts of the question, some options come close. Option C is the closest since it contains the empty set and the set itself, which are parts of the power set, however, it fails to list all of the subsets. Thus, specifically for this question and the options provided, none of the choices are correct if we consider the conventional meaning of a power set in set theory.