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"The United States' [relationship] with China and Taiwan"
"The United States' [relationships] with China and Taiwan."

Are both correct? We are talking about two different relationships here. Thank you.
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Given the differences between the two, they can certainly be considered as separate relationships.

The United States' relationships with China and Taiwan …
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Hi,

Are you implying that if the two countries in question are both close to the United States, I can say:

"The United States' relationship with Britain and Canada"?

Or should still use the plural form of the word?
SuperESLAre you implying that if the two countries in question are both close to the United States, I can say:
"The United States' relationship with Britain and Canada"?
Actually, my reasoning was that although Taiwan is (arguably) a part of China they are very different from each other; therefore the sentence makes sense. However, if the sentence described a relationship(ѕ) with a country and an integral part of that country, the sentence would of course would not make sense:

India's relationship(ѕ) with The United States and California…

As for your new example, I would use relationships, unless Britain and Canada were somehow in league with each other.
Thank you, Aspara Gus. By the way, I have a question that has been left unanswered on another thread (perhaps people find it too long to bother to respond to it). Do you think you can take the time to go through and just give me some simple yes and no answers? Thank you.

(1) "The objective of this essay is to illuminate an aspect of early Communist rule in Poland whose ephemeral moments [have been] prone to being overshadowed by later events."

(2) "The objective of this essay is to illuminate an aspect of early Communist rule in Poland whose ephemeral moments [are] prone to being overshadowed by later events."

(3) "The objective of this essay is to illuminate an aspect of early Communist rule in Poland whose ephemeral moments [were] prone to being overshadowed by later events."

What difference would it make to the implied meaning of the sentence whether I use [have been] or [are] or [were]? My attempt:

In sentence (1) the implied meaning is that historically, ever since the early period of Communist rule in Poland, people [commentators, scholars, everyone etc.] have always tended to overlook this 'aspect' of it.

In sentence (2) the implied meaning is that people nowadays tend to overlook this aspect of early Communist rule in Poland but that in the past [the period between then and now] people did not.

In sentence (3) the implied meaning is that people tended to overlook this aspect of early Communist rule in Poland in the past but people nowadays no longer overlook it.

Is this how I should grasp the difference in implied meanings between the three sentences? So all three sentences are equally grammatically tenable, only that they have different implied meanings?
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SuperESLIn sentence (1) the implied meaning is that historically, ever since the early period of Communist rule in Poland, people [commentators, scholars, everyone etc.] have always tended to overlook this 'aspect' of it.
No, there's a difference between have been and have always been. Besides, we don't know if people really overlook the moments; all we know is that they are prone (likely / subject / open to be) overshadowed by later events.
SuperESLIn sentence (2) the implied meaning is that people nowadays tend to overlook this aspect of early Communist rule in Poland but that in the past [the period between then and now] people did not.
Yes, are does suggest nowadays.
SuperESLIn sentence (3) the implied meaning is that people tended to overlook this aspect of early Communist rule in Poland in the past but people nowadays no longer overlook it.
We don't know this. The past tense tells us only about the past and nothing about the present.
SuperESLSo all three sentences are equally grammatically tenable, only that they have different implied meanings?
I can't argue with this.