If `mu = { 0,1,2,3,4,5,6,7,8,9}` , X = {2,3,5,7} and Y = {2,5,8} . Find n ` (X cup Y)`.

Options

A. 5
B. 7
C. 6
D. 9

Answer

To solve the problem, we need to find the number of elements in the union of sets X and Y. Let's go through the steps one by one.

### Step 1: Identify the Sets
We have the following sets:
- Universal set, \( \mu = \{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\} \)
- Set \( X = \{2, 3, 5, 7\} \)
- Set \( Y = \{2, 5, 8\} \)

### Step 2: Find the Union of Sets X and Y
The union of two sets, denoted as \( X \cup Y \), includes all the elements that are in either set X or set Y, without duplicates.

- Elements in \( X \): 2, 3, 5, 7
- Elements in \( Y \): 2, 5, 8

Now, we combine these sets:
- From \( X \): 2, 3, 5, 7
- From \( Y \): 2 (already counted), 5 (already counted), 8

So, the union \( X \cup Y \) will be:
\[ X \cup Y = \{2, 3, 5, 7, 8\} \]

### Step 3: Count the Number of Elements in the Union
Now, we need to count the number of distinct elements in the union \( X \cup Y \):
- The elements are: 2, 3, 5, 7, 8

Counting these, we find that there are 5 distinct elements.

### Conclusion
Thus, the number of elements in \( X \cup Y \) is:
\[ n(X \cup Y) = 5 \]

### Final Answer
The answer is \( n(X \cup Y) = 5 \).

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