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