Q:

Problem with logical operators precedence

I'm studying logical operators for school and there's a weird question that keeps bugging me even though it seems pretty basic.

I was asked to evaluate the proposition : p -> q -> r with p, r are False and q is True.

I tried evaluating it from left to right like this: ( ( p -> q ) -> r ) and got wrong answer. 

Then, I checked my result with an online tool at https://web.stanford.edu/class/cs103/tools/truth-table-tool/ and it evaluates the proposition from right to left like this:  ( p -> ( q -> r ) ) ( you can see in this picture ). I tried calculating the result again with this order and it was accepted as right answer !

That's really odd because my lecturer said that if operators are at the same level then the proposition should be evaluated from left to right. Have I misunderstood something ? 

A:

Well, the operations $\wedge,\vee,\Leftrightarrow$ are left-associative while the operation $\Rightarrow$ is right-associative.
So
$[p\Rightarrow q\Rightarrow r ]\Longleftrightarrow [p\Rightarrow (q\Rightarrow r)].$

