Let the relations R_{1} and R_{2} on the set X = { 1,2,3,...,20} be given by R_{1} = {(x,y):2x - 3y = 2} and R_{2} = {(x,y) : - 5x + 4y = 0}. If M and N be the minimum number of elements required to be added in R_{1} and R_{2}, respectively, in order to make the relations symmetric, then M + N equals

Question

Let the relations R_1 and R_2 on the set X = \ 1,2,3, ... ,20\ be given by R_1 = \(x,y):2x - 3y = 2\ and R_2 = \(x,y) : - 5x + 4y = 0\. If M and N be the minimum number of elements required to be added in R_1 and R_2, respectively, in order to make the relations symmetric, then M + N equals

DivineJEE · Accepted Answer

(a) : R_1 = \(x,y):2x - 3y = 2\ R_1 = \(4,2),(7,4),(10,6),(13,8),(16,10),(19,12)\ So, 6 elements are needed to make R_1 symmetric\ => M = 6R_2 = \(x,y): - 5x + 4y = 0\ R_2 = \(4,5),(8,10),(12,15),(16,20)\ So, 4 elements are needed to make R_2 symmetric\ => N = 4Therefore M + N = 6 + 4 = 10

Explanation

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