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Which one of the following is the correct form? For some reason, I have trouble understanding whether the correct form depends on "a necessary condition" (is) or "changes" (are).

A necessary condition are training-induced changes in ...

or

A necessary condition is training-induced changes in ..

What is the logic to decide which one is correct?

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    The subject of the sentence is the noun phrase a necessary condition. A can only be used with a singular noun phrase. SIngular noun phrases acting as subjects take singular verbs. Are is not a singular verb, but is is. You figure it out. – John Lawler May 5 '15 at 19:27
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    To reduce confusion caused by distracting details, simplify the examples, then judge. "A condition is/are changes." – Greg Lee May 5 '15 at 19:55
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"A necessary condition" is the subject and it is singular, so the correct verb is "is".

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