n(A)=20, n(B)=18 and `n(A cap B)=5`, then `n(A cup B)` is

Options

A. 23
B. 33
C. 26
D. 40

Answer

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

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

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 sets A and B.

Given:
- \( n(A) = 20 \)
- \( n(B) = 18 \)
- \( n(A \cap B) = 5 \)

Now, we can substitute these values into the formula:

1. Calculate \( n(A) + n(B) \):
\[ n(A) + n(B) = 20 + 18 = 38 \]

2. Subtract \( n(A \cap B) \) from the sum:
\[ n(A \cup B) = 38 - n(A \cap B) = 38 - 5 = 33 \]

Thus, the number of elements in the union of sets A and B is:
\[ n(A \cup B) = 33 \]

### Final Answer:
The number of elements in \( A \cup B \) is 33.

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