Let the relations \({R}_{1}\) and \({R}_{2}\) on the set \(X={1,2,3,\ldots .,20}\) be given by \({R}_{1}={(x,y):2x-3y=2}…

Let the relations \({R}_{1}\) and \({R}_{2}\) on the set \(X={1,2,3,\ldots .,20}\) 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

[JEE Main 2024, 6 Apr (Shift 1)]