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Question 1.
I found the following example sentence in Longman Dictionary of Contemporary English: She was finally evicted in April for non-payment of rent.
Is it optional to put "the" between "for" and "non-payment"?
She was finally evicted in April for the non-payment of rent.
Question 2
According to a Japanese website for English learning, the following sentences are both acceptable and there is no difference in meaning between them.
The closure of a factory causes hardship to everyone involved.
Closure of a factory causes hardship to everyone involved.
But the definite article before "closure" is required in the following case.
The closure of that factory caused hardship to all of them.
Wrong: Closure of that factory caused hardship to all of them.
Does it mean that "the" is required before "closure of that factory" because the sentence mentions "that factory" (not just any factory)?