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Let's break down the problem step by step based on the image you've uploaded.

We have seven tiles, each labeled with a different letter from the first seven letters of the alphabet: A, B, C, D, E, F, G. 

### Definitions of Events:
- **Event X**: The letter selected is found in the word "BAG". This means the possible outcomes for **X** are letters **B, A, G**.
- **Event Y**: The letter selected comes after "C". This means **Y** consists of letters **D, E, F, G** (since these letters come after C in the alphabet).

Now, let's answer each part:

### (a) Event "X or Y":
This asks for the union of sets X and Y, meaning any letter that is in either X, Y, or both. 

- **X** = {B, A, G}
- **Y** = {D, E, F, G}

The union (X or Y) is all the unique letters from both sets:
\[ X \cup Y = \{A, B, D, E, F, G\} \]

### (b) Event "X and Y":
This asks for the intersection of sets X and Y, meaning any letter that is in both X and Y.

- **X** = {B, A, G}
- **Y** = {D, E, F, G}

The intersection (X and Y) is only the common letters between the two sets:
\[ X \cap Y = \{G\} \]

### (c) The complement of event X:
The complement of X is the set of letters not in X. The full set of letters is {A, B, C, D, E, F, G}, so the complement of X will include any letter from this set that is not in {B, A, G}.

Thus, the complement of X is:
\[ X^c = \{C, D, E, F\} \]

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### Summary of Answers:
- **(a) X or Y**: {A, B, D, E, F, G}
- **(b) X and Y**: {G}
- **(c) Complement of X**: {C, D, E, F}

Would you like any further details or clarification on any part of this?

Here are 5 related questions for practice:
1. If the event was "Y and not X," what would the outcomes be?
2. What would the union of X and the complement of Y be?
3. How many elements are in the complement of Y?
4. What is the probability of drawing a letter in event X if each letter is equally likely?
5. What is the intersection of the complement of X and complement of Y?

**Tip:** When working with sets, it’s helpful to visualize them using Venn diagrams to clearly see unions, intersections, and complements.

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 'BAG'. Event Y: The letter selected comes after 'C'. Give the outcomes for each of the following events: (a) Event 'X or Y', (b) Event 'X and Y', (c) The complement of event X.

Learn how to solve a set theory problem involving the first seven letters of the alphabet. This example demonstrates the union, intersection, and complement of events with detailed solutions. Suitable for students in Grades 7-9.

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