Let A = { 0,3,4,6,7,8,9,10} and R be the relation defined on

A such that R = {(x,y) in 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 .

Question

Let A = \ 0,3,4,6,7,8,9,10\ and R be the relation defined on A such that R = \(x,y) in 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 .

DivineJEE · Accepted Answer

(19): A = \ 0,3,4,6,7,8,9,10\ R = \(x,y) in A x A:x - y is odd positive integer or x - y = 2\ Therefore Possible pairs to be added are \(0,3),(0,7),(0,9), (3,4),(3,6),(3,8),(3,10),(4,7),(4,9),(6,7),(6,9), (7,8),(7,10),(8,9),(9,10),(4,6),(6,8),(7,9),(8,10)\ Therefore We need to add minimum 19 elements to form it symmetric.

Explanation

The minimum number of elements that must be added to the relation R = {(a,b),(b,c),(b,d)} on the set { a,b,c,d} so that it is an equivalence relation is

Let R be the set of real numbers. end{enumerate} Statement-1: A = {(x,y) in R X R:y - x is an integer } is an equivalence . relation on R. Statement-2: B = {(x,y) in R X R:x = alpha y for some rational number } is . an equivalence relation on R.

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