Let \(R\) be a relation such that \(R = \{ (x,y) \in \mathbb{N \times \mathbb{N} \mid x+y \le 7 \}\). Minimum no. of elements to be added in \(R\) so that it becomes transitive is:
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To check for transitivity in a finite set, look for "chains": if you have (a,b) and (b,c), but the sum of (a,c) exceeds the boundary, that (a,c) is a mandatory addition for the transitive closure.