If A and B are two sets such that No. of elements in A, B and `A cap B` are 20,35 and 12 respectively, then find the number of elements in `A cup B`.

Answer

To find the number of elements in the union of two sets A and B, we can use the formula:

\[ N(A \cup B) = N(A) + N(B) - N(A \cap B) \]

Where:
- \( N(A \cup B) \) is the number of elements in the union of sets A and B.
- \( N(A) \) 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 sets A and B.

### Step-by-step Solution:

1. **Identify the given values:**
- Number of elements in set A, \( N(A) = 20 \)
- Number of elements in set B, \( N(B) = 35 \)
- Number of elements in the intersection of sets A and B, \( N(A \cap B) = 12 \)

2. **Substitute the values into the formula:**
\[ N(A \cup B) = N(A) + N(B) - N(A \cap B) \]
\[ N(A \cup B) = 20 + 35 - 12 \]

3. **Calculate the sum of \( N(A) \) and \( N(B) \):**
\[ 20 + 35 = 55 \]

4. **Subtract the number of elements in the intersection from the sum:**
\[ 55 - 12 = 43 \]

5. **Final Result:**
\[ N(A \cup B) = 43 \]

Thus, the number of elements in \( A \cup B \) is **43**.