Answer:
the one the question is refering to.
The writing 'rule' (myth) Churchill's reply satirizes is the 'Never end a sentence on a preposition' rule (i.g. as I intetionally did on the immediate sentence before this one). And his reply to it was something like 'This is the type of errant pedantry up with which I will not put.'
The 'rule' is a myth, yes, but of course what Churchill did was an exaggeration to sneeringly point out the ignorance of those who criticized him.
His sentence therefore was incorrect. One possible change to improve it could be: 'This is the type of errant pedantry which I will not put up with.'
Specially the 'up' and 'with' of 'put up with' could never go in the middle of a sentence, as 'put up with' is a phrasal verb, meaning the verb and the preposition must always be together in the correct order.
I was able to find some possible variations of what his sentence could have actually had been, but in none of them the 'up with' goes along with 'put', so either ways we can assume that his sentence was deliberately wrong.
Explanation:
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