x y x ySolution1 Let xy and uv be in the set xyuvxuyv xuyu

{(x, y) | x = y}

Solution

1. Let, (x,y) and (u,v) be in the set

(x,y)+(u,v)=(x+u,y+v)

x+u=y+u=y+v

HEnce, set is closed under addition

2. Let, c be a scalar, (x,y) be in the set

c(x,y)=(cx,cy)

cx=cy

So, set is closed under scalar multiplication

The subset is the line: y=x