"For every x (in the domain), there is at least one y (in the domain) that can depend on x and may be equal to x such that L(x, y) is true"

• $\forall$ x $\exists$ y L(x, y)
• Everyone loves someone (e.g. their family)

"There is at least one y such that for every x (including the case y=x), L(x, y) is true"

• $\exists$ y $\forall$ x L(x, y)
• There is someone everyone loves (e.g. santa)