Let R = (x, y) N N : _e(x + y) 2 . Then the minimum number of elements, required to be added in R to make it a transitive relation, is __________.

Step-by-step solution

Given the relation R = (x, y) N N : _e(x + y) 2 . This condition simplifies to: x + y e^2 Since e 2.718 , we have e^2 7.389 . As x, y N , the sum x + y must be a natural number. Therefore, the condition becomes: x + y 7 Let's find the number of elements in R by listing the possible pairs (x, y) : For x = 1 , y 1, 2, 3, 4, 5, 6 (6 elements) For x = 2 , y 1, 2, 3, 4, 5 (5 elements) For x = 3 , y 1, 2, 3, 4 (4 elements) For x = 4 , y 1, 2, 3 (3 elements) For x = 5 , y 1, 2 (2 elements) For x = 6 , y 1 (1 element) Tota