No. "countable nouns , which are used with a or an or a number and have a plural: car, soldier" It means all countable nouns on earth are used with a, an or a number, and have a plural. By the same token, your second sentence is false too.
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I think the above grammar codes should be rewritten as the following:Yes. Given the context you describe, I certainly would think so.
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Am I right?