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Canada does not require that U.S. citizens obtain passports to enter the country, and ----------------.

(a) Mexico does neither

(b) Mexico doesn't either

(c) neither Mexico does

(d) either does Mexico.

(e) Neither does Mexico

The answer is (b) or (e). The explanation in the TOEFL book is not upto my understanding. Would you please explain the reason and rule behind the answers?
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Just as "too" is added to a second, similar affirmative statement, "either" is added to a second, similar negative statement. The two cannot be interchanged. In this pattern two different subjects have the same predicate.

Canada requires this, and Mexico requires this [too / *either].
Canada doesn't require this, and Mexico doesn't require this [either / *too].

We can shorten the second negative in two different ways.

(1) Leave out the words after the negative and before "either"
Canada doesn't require this, and Mexico doesn't ............either.

(2) Substitute "and neither + verb + subject" for "and + subject + verb + ..." (leaving out the same words as in (1)) Note: The "not" or "n't" is not counted as part of the verb.
Canada doesn't require this, and neither does Mexico.

Here are more examples of these two ways of shortening the second of two negatives.

I don't like anchovies on pizza, and my friends don't like anchovies on pizza (either).
I don't like anchovies on pizza, and my friends don't either.
I don't like anchovies on pizza, and neither do my friends.

My brother can't read Arabic, and I can't read Arabic (either).
My brother can't read Arabic, and I can't either.
My brother can't read Arabic, and neither can I.

The House of Representatives has not approved that legislation, and the Senate has not approved that legislation (either).
The House of Representatives has not approved that legislation, and the Senate has not either.
The House of Representatives has not approved that legislation, and neither has the Senate.

I hope that helps.

CJ
Comments  
I think " either " use after two negative verbs.

Canada does not require the U.S citizens obtain passports to enter the country,and Mexico doesnt either.

Neither use in front of modal or auxliary in that sentence. it is sort of invertsion.
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 CalifJim's reply was promoted to an answer.
Thanks, CalifJim. Your explanation is very informative, so that the students like me can understand the concepts easily and quickly.
Thanks much for your feedback, Welkins2139.
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the first part of the sentence depicts negation, so the answer expected should also be in negation. Use of NEITHER is more appropriate. followed by do/does which in turn is followed by the subject.

for e.g....... I dont like coffee. Neither does he.

neither does mexico