Originally Posted by

**MoeBlee** Oops, sorry I missed that you did negate at your first line.

As to parentheses, I just took the informality of eliminating a lot unnecessary parentheses.

But there's a technical point (pedantic but nevertheless it is best to be precise) (and it might be a problem with the wording of the problem itself): The negation of a formula F is ~F. So when asked to negate a formula, we don't have to go on also to mention other equivalents derived by such things as DeMorgan's laws and quantifier exchange. In fact, those extra equivalents are NOT the negation of your original formula. They are EQUIVALENTS of the negation but are not themselves the negation.

That is to say, if I answered that question on a test, I would just put the negation sign on the outside of the formula and move on to the next question. If the professor said that I'm wrong because I didn't transform further, then I'd tell him that he's wrong. The negation of a formula F is ~F period, and any other transformation gives an EQUIVALENT of the negation but not the negation ITSELF. If asked to negate F, the correct answer is to write ~F.