Which of the following two sentences is correct?
- The teacher, and not the students, is speaking.
- The teacher, and not the students, are speaking.
Which of the following two sentences is correct?
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Both sentences are wrong, but option 1 is less wrong.
Option 2 is totally wrong. A clause surrounded by commas is optional; the sentence must stand on its own without it. Option 2 cannot be correct because "the teacher are speaking" makes no sense.
Option 1 isn't great either. A clause surrounded by commas is used to add a side note that helps, but is not needed by, the rest of the sentence. "and not the students" does not qualify the teacher (who is obviously not the students) or speaking (because subjects own verbs, not the other way around). What you have is not one qualified thought, but two separate thoughts.
A better option is "The teacher is speaking; the students are not."