Question

If $A$ and $B$ are two sets such that $n(A) = 17, n(B) = 23$ and $n(A \cup B) = 38$, then $n(A \cap B)$ is:

• A. 2
• B. 4
• C. 6
• D. 8

Hint:

[Image of Venn diagram for two sets A and B] The intersection is the overlap region counted twice when adding $n(A)$ and $n(B)$.

Answer 1

The Correct Option is A

Step 1: Concept
Use the Principle of Inclusion-Exclusion: $n(A \cup B) = n(A) + n(B) - n(A \cap B)$.
Step 2: Analysis
$38 = 17 + 23 - n(A \cap B)$. $38 = 40 - n(A \cap B)$.
Step 3: Conclusion
$n(A \cap B) = 40 - 38 = 2$.
Final Answer: (A)