A tile is selected from seven tiles, each labeled with a different letter from the first seven letters of the alphabet. The letter selected will be recorded as the outcome. Consider the following events. Event \( X: \) The letter selected is found in the word " \( B E A D^{\text {" }} \). Event \( Y: \) The letter selected comes after " \( D \) ". 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 " \( X \) and \( Y \) ": \{[i]) (b) Event \( { }^{n} X \) or \( Y *:\{D\} \) (c) The complement of the event \( Y:\{\square\} \)

Let's break down the events based on the letters available and the definitions given. (a) Event \( X \) specifies letters found in "BEAD," which are \( B, E, A, D \). Event \( Y \) includes letters that come after "D," which are \( E, F, G \). The intersection of these two sets (where both events happen) is simply the letters that are both in "BEAD" and come after "D." The only letter that satisfies this condition is: **\{E\}** (b) The event “not \( X \)” corresponds to the letters that are *not* in "BEAD" from the set of letters \( \{A, B, C, D, E, F, G\} \). Therefore, the letters in \( { }^{n} X \) include \( C, F, G \). Adding the letters in \( Y \), which are \( E, F, G \), the union of these events results in: **\{C, E, F, G\}** (c) The complement of the event \( Y \) includes the letters that do not come after “D.” From our set \( \{A, B, C, D, E, F, G\} \), the letters before and including \( D \) are: **\{A, B, C, D\}**