Q72 / 180 · COMEDK 2025 (10 May Shift 1) · Mathematics
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$0$
- B$7$
- Correct answerC$3$
- D$10$
Solution
Given that $A \subseteq B$, every element of set $A$ is also an element of set $B$.
By definition of intersection, $A \cap B = \{x : x \in A \text{ and } x \in B\}$.
Since $A \subseteq B$, for any $x \in A$, it follows that $x \in B$. Therefore, $A \cap B = A$.
The number of elements in $A \cap B$ is equal to $n(A \cap B) = n(A)$.
Given $n(A) = 3$, it follows that $n(A \cap B) = 3$.
Answer: $3$
By definition of intersection, $A \cap B = \{x : x \in A \text{ and } x \in B\}$.
Since $A \subseteq B$, for any $x \in A$, it follows that $x \in B$. Therefore, $A \cap B = A$.
The number of elements in $A \cap B$ is equal to $n(A \cap B) = n(A)$.
Given $n(A) = 3$, it follows that $n(A \cap B) = 3$.
Answer: $3$
Hence, the correct answer is option: 'C'.