Sets, Relations & Functions
Set Cardinality
Grade 11
Question:
<p>If elements in <span class='formula'>B_1, B_2, \ldots, B_n</span> are not repeated, the total number of elements is <span class='formula'>3n</span> but each element is repeated 9 times. If <span class='formula'>S = 15</span> (from equation (i)), find <span class='formula'>n</span>.</p>
Step-by-Step Solution
Key Concept: Set up an equation using the given relationship between the total number of elements, repetition count, and the sum S.
<p><strong>Solution:</strong></p><p>Given that total number of elements is <span class='formula'>3n</span> and each element is repeated 9 times:</p><p><span class='formula'>S = \frac{3n}{9}</span></p><p>From equation (i), we have <span class='formula'>S = 15</span>.</p><p>Therefore:</p><p><span class='formula'>15 = \frac{3n}{9}</span></p><p><span class='formula'>15 = \frac{n}{3}</span></p><p><span class='formula'>n = 45</span></p><p>∴ The answer is <strong>45</strong>.</p>
Correct Answer: 45