If n(X)= 4, n(Y)= 9, and the sets X and Y are disjoint, then find `n(XuuY)`.

Answer

To find the number of elements in the union of two disjoint sets \(X\) and \(Y\), we can follow these steps:

### Step 1: Identify the number of elements in each set
We are given:
- \(n(X) = 4\) (the number of elements in set \(X\))
- \(n(Y) = 9\) (the number of elements in set \(Y\))

### Step 2: Understand the concept of disjoint sets
Disjoint sets are sets that have no elements in common. This means:
- \(n(X \cap Y) = 0\) (the number of elements in the intersection of sets \(X\) and \(Y\))

### Step 3: Use the formula for the union of two sets
The formula for the number of elements in the union of two sets is given by:
\[ n(X \cup Y) = n(X) + n(Y) - n(X \cap Y) \]

### Step 4: Substitute the known values into the formula
Substituting the values we have:
\[ n(X \cup Y) = n(X) + n(Y) - n(X \cap Y) \]
\[ n(X \cup Y) = 4 + 9 - 0 \]

### Step 5: Calculate the result
Now, perform the addition:
\[ n(X \cup Y) = 4 + 9 = 13 \]

### Final Answer
Thus, the number of elements in the union of sets \(X\) and \(Y\) is:
\[ n(X \cup Y) = 13 \]

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