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I am given two statements:

Either Alice or Bob is in the room.

Either Alice or Bob isn't in the room.

I would represent them as follows:

(A ∨ B)

¬(A ∨ B)

My question is whether the two statements are equivalent. By the first statement, if Bob is in the room, Alice isn't. By the second, if Alice isn't in the room, Bob is. These are converses of each other. Can one represent them with the same formula since they mean the same thing?