Let A ={0, 3,4,6, 7, 8, 9,10} and R be the relation defined on A such that R{(x, y) 
A x A : x – y is odd positive integer or x - y = 2}. The minimum number of elements that must be added to the relation R, so that it is a symmetric relation, is equal to__________
Text Solution
Verified by Experts19
(19)
Given,
Set A ={10,9,8,7,6,4,3,0}
Now relation x-y is odd or x-y = 2 can be given by,
{R = (10,9), (10,8), (10,7), (10,3), (9,8), (9,7), (9,6), (9,4), (9,0), (8,7), (8,6), (8,3), (7,6), (7,4), (7,0), (6,4), (6,3), (4,3), (3,0)}
So, total there are 19 elements and all the elements of R, (a, b) are of type a > b.
Hence, we need to add total of 19 more elements to R to make in symmetric
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