I'm reading A Logical Approach to Discrete Math by David Gries and Fred B. Schneider and I got all snagged up on an apparent contradiction on an elementary point. On page 35, they write:
For example, consider the sentence "If you don't eat your spinach, I'll spank you". Using variable $es$ for "you eat your spinach" and variable $sy$ for "I'll spank you", we translate this as $\neg{es}\;\Rightarrow\;{sy}$. Note that this expression is true if you eat your spinach, i.e., if $\neg{es}$ is false then so is $\neg{es}\;\Rightarrow\;{sy}$.
The statement "This expression is true if you eat your spinach" should mean that
$$\neg{es}\;\Rightarrow\;{sy}$$
is true if $\neg{es}$ is false. That means $es$ is true and the implication is true no matter what the value of $sy$ because the implication is equivalent to $es\vee{sy}$. If you eat your spinach, then you may still get spanked, or not. This looks right to me.
The author's next phrase seems to contradict that: "if $\neg{es}$ is false then so is $\neg{es}\;\Rightarrow\;{sy}$". Huh?
Is there some meta-level on which I should be interpreting that last (seemingly incorrect) phrase, or is this just a typo? I'm asking this question because the contradiction is so blaring and blatant that a typo doesn't seem plausible in this place.