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Let \( R \) be a relation such that \( R = \{ (x, y) \in \mathbb{N} \times \mathbb{N} \mid x + y \le 7 \} \). Minimum number 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.

Updated On: Apr 8, 2026

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The Correct Option is C

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Let \( R \) be a relation such that \( R = \{ (x, y) \in \mathbb{N} \times \mathbb{N} \mid x + y \le 7 \} \). Minimum number of elements to be added in \( R \) so that it becomes transitive is:

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The Correct Option is C

Solution and Explanation

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