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 " $$ A $$ or $$ B^{n}: \mid\{| |\} $$ (b) Event " $$ A $$ and $$ B $$ ": \{ (c) The complement of the event $$ A $$; $$ \square $$ Start ower

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(a) $$A$$ or $$B$$ : The outcomes in event $$A$$ are $$\{2, 4, 6\}$$, and the outcomes in event $$B$$ are $$\{1, 2, 3\}$$. Their union is  
$$
\{2, 4, 6\} \cup \{1, 2, 3\} = \{1, 2, 3, 4, 6\}.
$$

(b) $$A$$ and $$B$$ : The intersection of $$\{2, 4, 6\}$$ and $$\{1, 2, 3\}$$ is  
$$
\{2, 4, 6\} \cap \{1, 2, 3\} = \{2\}.
$$

(c) The complement of the event $$A$$ : The complement contains outcomes not in $$A$$, so from the total outcome space $$\{1, 2, 3, 4, 5, 6\}$$ removing $$\{2, 4, 6\}$$ gives  
$$
\{1, 2, 3, 4, 5, 6\} \setminus \{2, 4, 6\} = \{1, 3, 5\}.
$$
(a) Event "A or B": 1, 2, 3, 4, 6 (b) Event "A and B": 2 (c) Complement of event A: 1, 3, 5

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