Correct : c

The correct answer is Option C - 0.
The Jaccard coefficient between two sets A and B is defined as |A ∩ B| / |A ∪ B|. To find the lowest possible value, we need to minimise the number of shared edges between any two spanning trees of K_n.
Key properties: Every spanning tree of K_n has exactly n−1 edges. K_n has n(n−1)/2 total edges.
Can two spanning trees share zero edges? Yes - by the Nash-Williams theorem, a graph G contains k edge-disjoint spanning trees if and only if for every partition of vertices into r parts, the number of edges crossing between parts is at least k(r−1). For K_n with n > 4, ⌊n/2⌋ ≥ 2, guaranteeing the existence of at least two fully edge-disjoint spanning trees.
When T₁ and T₂ are edge-disjoint: |T₁ ∩ T₂| = 0, so Jaccard = 0 / |T₁ ∪ T₂| = 0.
Why the other options are wrong:
Option A (1/n): This would require exactly 1 shared edge and union of size n - not the minimum achievable. Incorrect.
Option B (1/(2n−3)): This would correspond to 1 shared edge out of 2n−3 total - again not the minimum. Incorrect.
Option D (1/(n−1)): This would mean 1 shared edge out of n−1 total - still positive, and not the minimum. Incorrect.
Since two fully edge-disjoint spanning trees always exist in K_n for n > 4, the lowest possible Jaccard coefficient is 0.