Trigonometry & Inverse Trigonometry
General
Grade 11
Question:
<p>Total reflexive relations on <span class="math-inline">\(A\)</span> (<span class="math-inline">\(|A|=n\)</span>):</p>
<strong>2^(n²-n)</strong>
2^(n²)
2^(n²-n+1)
2^(n²+n)
Step-by-Step Solution
Key Concept: General
<div class="solution"><p>Total pairs = <span class="math-inline">$n^2$</span>. Diagonal <span class="math-inline">$n$</span> pairs must be included (reflexivity). Remaining <span class="math-inline">$n^2-n$</span> pairs: 2 choices each. Total = <span class="math-inline">$2^{n^2-n}$</span>.</p><p><strong>Answer: (A) <span class="math-inline">$2^{n^2-n}$</span></strong></p><div class="trap-box"><strong>Trap:</strong> Treating diagonal pairs as optional — they are forced in reflexive relations.</div><div class="key-concept"><strong>Key Concept:</strong> Reflexivity forces all diagonal entries; count free off-diagonal entries</div></div>
Correct Answer: 1