On a homework assignment, we were given
$$x \lt 5y \leftrightarrow x \gt z \rightarrow x + z \geq yw \wedge -x \lt z$$
I broke it up into
$$1~~~x <5y$$ $$2~~~~~x > z$$ $$3~~~x + z \geq yw \wedge -x \lt z$$
The difficulty comes in which order to parse the sections. I don't know how to draw a tree in Latex, but I argued that $\leftrightarrow$ should be a the root and the $\rightarrow$ should be at the first right node. My friends argue that the $\rightarrow$ should be at the root, and the $\leftrightarrow$ should be at the first left node.
My reasoning is that with operators of equal precedence and lack of initial parenthesization, left associativity comes into play, thus rendering $\leftrightarrow$ as the root. My friends argue that parenthesizing the formula results in sections 2 and 3 together, thus making $\rightarrow$ the root.