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「挑発に乗る」 and 「挑発に対応する」 both sound to me like: "`To respond to a provocation.`"

Is this correct? Any important differences?

--- extra question #2 ---

As per the given answer, 「挑発に乗る」 is to respond irrationally. That makes sense
because it is a metaphor.

What about negating both phrases?

「挑発に乗らなかった」 means `to not respond to provocation (in an *irrational* manner)`  
「挑発に対応しなかった」 means `to no respond to provocation (in a *rational* manner)`

Ultimately, could I say something like:

> 田中さんの挑発に乗らなかったにしても、対応した。

means:

> I didn't let Tanaka provoke me into an irrational response. Rather, I
> countered his provocations in a measured tone.
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word-choice
Is「挑発に対応しなかった」another way to say「挑発に乗らなかった」?
In fact, they are quite different.

If you 「挑発に乗る」, you respond to a provocation in the way it was intended for;
you lose your head and do things you otherwise wouldn't.

「挑発に対応する」 would mean _to deal with_ a provocation, likely in a calm and
sensible manner.

--- Answer to extra question #2 ---

How I see them:

・「挑発に乗らない」= not respond to provocation in an irrational manner (may or may not
do what is rational)

・「挑発に対応しない」= not respond to provocation in any way (= flatly ignore it )

Though you _could_ say the following:

> 田中さんの挑発に乗らなかったにしても、対応した。

I find the phrasing somewhat awkward. If I were to rewrite it, I might go for
something like:

> 田中さんの[挑発に(は)乗らず/挑発に乗ること(は)なく]、冷静に対応した。

--- EDIT ---

One important distinction between the two I failed to mention earlier is that
「挑発に乗る」 is an idiomatic phrase while 「挑発に対応する」 is not.

Theoretically, there is no semantic incongruity in the phrase 「挑発に対応する」. In
practical terms, however, it's much less likely to appear as-is (or otherwise)
than 「挑発に乗る」, but instead often comes accompanied by a modifier specifying how
the responding is done, like _冷静に_.
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挑発に乗る means you respond to a provocation / challenge of others without
discretion, or in the way the aggressor or provoker plotted. In Japanese, we
respond to provocation but don't 'deal with' provocation. You can't be willy-
nilly against a challenge or aggression directed to you. You should be
resolute to the provocation, and your choice is either 挑発に乗る / 挑発に応じる
/挑発を受けて立つ / or 挑発に乗らない / 挑発に応じない / 挑発を退ける。

I haven't heard the turn of phrase 挑発に"対応する" so often. It somewhat doesn't sit
well with the word 挑発 to me.
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