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This question already has an answer here:

Is on needed a second time in this sentence?

  • There is a bad effect either on human health or environment.
  • There is a bad effect either on human health or on environment.

marked as duplicate by Edwin Ashworth, Dan Bron, tchrist, Nathaniel, MetaEd Aug 4 '16 at 20:42

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    The preposition may be omissible, but the definite article isn't—it's the environment (the one and only). – Janus Bahs Jacquet Jul 31 '16 at 19:31
  • In that sentence you can eliminate the second "on" because of a rule called conjunction reduction, where contingent repeated words before or after the clauses separated by a conjunction ("Or" in our case) can be shared among them. If you didn't have a conjunction between them, I believe you'd have to keep both. – Tonepoet Jul 31 '16 at 19:31
  • @Tonepoet You should make that an answer. – Janus Bahs Jacquet Jul 31 '16 at 19:32
  • @JanusBahsJacquet I'm hesitant to do that because the titular question is too vague in my opinion, but if you or anybody else wants the rep. and thinks it's appropriate, go ahead. – Tonepoet Jul 31 '16 at 19:34
  • Don't forget that the title of the question is only my interpretation of the original. (And actually, environment here could easily be "huiman environment" and another example of reduction.) – Andrew Leach Jul 31 '16 at 19:36
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The answer is that the second on is not needed, and may be deleted.
But that doesn't have anything to do with prepositions, really.
It works for just about any kind of word. Under the correct conditions, at least.

The name of the syntactic rule involved is Conjunction Reduction. It applies only to the second and following clauses in a compound sentence connected by a coordinate conjunction like and, or, but.

What it does is delete material -- adjectives, nouns, prepositions, you name it -- that's duplicated in the second and following clauses. Because it is duplicated, and therefore is redundant.

If you start with

  • There is a bad effect on A or there is a bad effect on B.

you can delete there is a bad effect on, which is repeated in both clauses,

  • There is a bad effect on A or B.

or you can delete less of the repeated material,

  • There is a bad effect on A or on B. (deleting there is a bad effect)
  • There is a bad effect on A or a bad effect on B. (deleting there is)
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I would change the sequence of the two words "either on" to "on either":

There is a bad effect on either human health or the environment.

By changing the word order to place "on" in front of "either", the question of whether to repeat "on" is rendered moot: the word then clearly applies to both "human health" and "the environment".

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