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Digital clocks tell the time with a set of numerals which appear/appears in a little window.

Please tell me which verb I should use in this sentence. Thank you so much.

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There is a little ambiguity in this sentence. It is possible for the verb "to appear" to refer to a set or to numerals. The verb that you choose subtly changes the meaning of the sentence.

A. Digital clocks tell the time with a set of numerals which appears in a little window.
B. Digital clocks tell the time with a set of numerals which appear in a little window.

Sentence A means that "a set appears in the window" and then describes that set as being composed of numerals.

Sentence B means that "numerals appear in the window" and then describes those numerals as being part of a set.

In this case I think that version B would be more appropriate. You could omit the information regarding a set and the sentence would still make sense, but if you omit the information about numerals it really doesn't. However, with both pieces of information present it is up to you which you choose.

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    But set can be plural when it refers to a plural thing, just like any other collective noun in English. A group of people are waiting for you.
    – tchrist
    Sep 25 '15 at 7:36
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The verb is driven by the noun "a set of numerals" not by numerals themselves. So "appears" would be good choice. This is similar to

An army of soldiers marches along.

Even though the soldiers March individually, we are talking about the army, not the soldiers.

Hope this helps.

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