Let X ={Ram , Geeta , Aakbar} be the set of students of XI class who are in School Hockey team.
Let Y= {Geeta , David ., Ashok } be the set of students of XI class who are in School Football team .
Find `XuuYandXcapYand` interpret the set .

Answer

To solve the problem, we need to find the union and intersection of the two sets \( X \) and \( Y \).

### Step 1: Define the Sets
Given:
- Set \( X = \{ \text{Ram}, \text{Geeta}, \text{Aakbar} \} \) (students in the Hockey team)
- Set \( Y = \{ \text{Geeta}, \text{David}, \text{Ashok} \} \) (students in the Football team)

### Step 2: Find the Union of Sets \( X \) and \( Y \)
The union of two sets \( X \) and \( Y \), denoted as \( X \cup Y \), includes all the elements from both sets, without repeating any elements.

- List the elements of \( X \): Ram, Geeta, Aakbar
- List the elements of \( Y \): Geeta, David, Ashok

Now, combine them:
- \( X \cup Y = \{ \text{Ram}, \text{Geeta}, \text{Aakbar}, \text{David}, \text{Ashok} \} \)

### Step 3: Find the Intersection of Sets \( X \) and \( Y \)
The intersection of two sets \( X \) and \( Y \), denoted as \( X \cap Y \), includes only the elements that are present in both sets.

- The common element in both sets is: Geeta

Thus,
- \( X \cap Y = \{ \text{Geeta} \} \)

### Step 4: Interpret the Sets
- **Interpretation of \( X \cup Y \)**: This set includes all students who are either in the Hockey team or in the Football team or in both. In this case, it represents students who play at least one of the two sports.

- **Interpretation of \( X \cap Y \)**: This set includes students who are in both teams. In this case, it represents students who play both Hockey and Football.

### Final Answer
- \( X \cup Y = \{ \text{Ram}, \text{Geeta}, \text{Aakbar}, \text{David}, \text{Ashok} \} \)
- \( X \cap Y = \{ \text{Geeta} \} \)

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