Sets, Relations & Functions
Number of elements in sets
Grade 11
<p>If \(n(A) = 3\), \(n(B) = 6\) and \(A \subseteq B\). Then the number of elements in \(A \cup B\) is equal to</p>
Step-by-Step Solution
Key Concept: When A ⊆ B (A is a subset of B), every element of A is already in B, so A ∪ B = B. Therefore, n(A ∪ B) = n(B).
<p><strong>Step 1:</strong> Given that A ⊆ B, this means every element of A is contained in B.</p><p><strong>Step 2:</strong> When forming A ∪ B, we combine all elements from both sets. Since A is already completely inside B, A ∪ B contains exactly the elements of B and nothing more.</p><p><strong>Step 3:</strong> Therefore, A ∪ B = B, which means n(A ∪ B) = n(B) = 6.</p><p><strong>Verification:</strong> Using the formula n(A ∪ B) = n(A) + n(B) − n(A ∩ B): Since A ⊆ B, we have A ∩ B = A, so n(A ∪ B) = 3 + 6 − 3 = 6 ✓</p><p>∴ Answer: 6 (Option C)</p>
Correct Answer: C