<p>Total symmetric relations on \(A\) (\(|A|=n\)):</p>
Step-by-Step Solution
<div class="solution"><p>Diagonal entries: $n$ free choices. Upper triangle: $n(n-1)/2$ free pairs (each determines its mirror). Total: $2^{n+n(n-1)/2}=2^{n(n+1)/2}$.</p><div class="key-concept"><strong>Key Concept:</strong> Symmetry identifies (i,j) with (j,i) -- count only one triangle plus diagonal
Correct Answer: 2^(n(n+1)/2)