If A and B are two disjoint sets `n(A) +n(B) = 16, ` then find `n(A cup B)`.

Options

A. 16
B. 18
C. 24
D. Cannot say

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the given information
We are given two disjoint sets A and B. This means that they have no elements in common.

### Step 2: Write down the formula for the union of two sets
The formula for the number of elements in the union of two sets A and B is:
\[ n(A \cup B) = n(A) + n(B) - n(A \cap B) \]
Where:
- \( n(A) \) is the number of elements in set A,
- \( n(B) \) is the number of elements in set B,
- \( n(A \cap B) \) is the number of elements in the intersection of A and B.

### Step 3: Substitute the known values into the formula
From the problem, we know:
- \( n(A) + n(B) = 16 \)
- Since A and B are disjoint, \( n(A \cap B) = 0 \).

Now, substituting these values into the formula:
\[ n(A \cup B) = n(A) + n(B) - n(A \cap B) \]
\[ n(A \cup B) = 16 - 0 \]

### Step 4: Calculate the result
Now, we can simplify the equation:
\[ n(A \cup B) = 16 \]

### Step 5: State the final answer
Thus, the number of elements in the union of sets A and B is:
\[ n(A \cup B) = 16 \]