Let the relations R_1 and R_2 on the set X={1,2,3, …., 20} be given by R_1={(x, y): 2 x-3 y=2} and R_2={(x, y):-5 x+4 y=0}. If M and N be the minimum…

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