A number cube with faces labeled 1 to 6 is rolled once. The number rolled will be recorded as the outcome. Consider the following events. Event \( A: \) The number rolled is even. Event \( B: \) The number rolled is less than 4 . Give the outcomes for each of the following events. If there is more than one element in the set, separate them with commas. (a) Event \( { }^{n} A \) or \( B^{*}:\{D\} \) (b) Event \( { }^{n} A \) and \( B^{*}:\{\square\} \) (c) The complement of the event \( A:\{\square\} \)

Let's explore the outcomes for each of the specified events related to the number cube roll. (a) Event \( A \) or \( B \): The outcomes for event \( A \) (the number rolled is even) are \( \{2, 4, 6\} \), and for event \( B \) (the number rolled is less than 4), the outcomes are \( \{1, 2, 3\} \). Combining these two sets, the outcomes for event \( A \) or \( B \) are: \( \{1, 2, 3, 4, 6\} \). (b) Event \( A \) and \( B \): Here, we find the overlap between the two events. The even numbers are \( \{2, 4, 6\} \), and the numbers less than 4 are \( \{1, 2, 3\} \). The common element where both events intersect is just \( \{2\} \), so the outcomes for event \( A \) and \( B \) are: \( \{2\} \). (c) The complement of the event \( A \): The outcomes for event \( A \) (even numbers) are \( \{2, 4, 6\} \). Therefore, the complement will include all outcomes that are not in event \( A \), which are the odd numbers, yielding: \( \{1, 3, 5\} \).