a$)$ Let $V=\{(x,y)$:$x,yF\}$ and $F$ be the field of real numbers. Show that $V$ is not a vector space with respect to addition and scalar multiplication as defined as

$($i$)(x,y)+(x_1,y_1)=(x+x_1,y+y_1)$

$($ii$)c(x,y)=(0,cy)$