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When I turn the sentence below into Subjunctive mood, which one is correct?

★Sentence I want to change :

*He is sad as he does not know that the problem has been solved

★Changed sentences (Which one is correct?) :

*If he knew that the problem has been solved, he would not be sad.

*If he knew that the problem had been solved, he would not be sad.

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The pattern that both changed sentences use is often called the second conditional (or Conditional 2). This has the past simple in the if-clause (protasis) and would + infinitive in the main clause_ (apodosis). Removing the embedded that clause results in both cases in:

If he knew, he would not be sad.

The tense of the that clause is not determined by the tense of the if-clause it is embedded in. It is determined by the usual considerations of which verb construction is most appropriate in the given context. In this case, it is the time frame in which the problem was, has been, had been, is being, will be, will have been solved. In other words:

  • If he knew that the problem had been solved, he would not be sad.
  • If he knew that the problem was solved (two months ago), he would not be sad.
  • If he knew that the problem has been solved, he would not be sad.
  • If he knew that the problem is being solved, he would not be sad.
  • If he knew that the problem will be solved, he would not be sad.
  • If he knew that the problem will have been solved (by the end of the month), he would not be sad.

As your original sentence uses the present perfect time frame for the solving of the problem, then the obvious way of restructuring the original sentence is:

If he knew that the problem has been solved, he would not be sad.

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