Question

If \( n(A) = 3 \) and \( n(B) = 7 \) and \( A \subseteq B \) then the number of elements in \( A \cap B \) is equal to

• A. 7
• B. 10
• C. 0
• D. 3

Hint:

If \( A \subseteq B \), then \( A \cap B = A \). Always use subset property directly.

Answer 1

The Correct Option is D

Step 1: Understand the given condition.
It is given that:
\[ A \subseteq B \]
This means every element of set \( A \) is also an element of set \( B \).

Step 2: Interpret the intersection.
Since all elements of \( A \) are already present in \( B \), the intersection becomes:
\[ A \cap B = A. \]

Step 3: Use the cardinality.
\[ n(A \cap B) = n(A). \]

Step 4: Substitute the given value.
\[ n(A) = 3. \]

Step 5: Conclude the result.
\[ n(A \cap B) = 3. \]

Step 6: Verify concept.
Whenever one set is a subset of another, their intersection equals the smaller set.

Step 7: Final conclusion.
Thus, the required number of elements is 3.
Final Answer:
\[ \boxed{3} \]