I'm currently working on some first order logic questions as a brush up for a discrete mathematics course and I'm having a bit of trouble remembering exactly how to find the negation of a logical statment. Precisely, how do I rewrite certain statements as the negated versions of themselves? I've had luck with a couple but right now I'm stumped on the following:
At the moment I'm working on an assignment for a discrete mathematics course and I've run into a question that seems deceptively simple based on how it is asked but I feel like the instructor is asking for more. The question goes as follows:
Give the negation of the statement ∃! x ∈ U [P(x)].
But to negate this statement could I not just put a ¬ in front of the equation and be done? I only ask because on this assignment most questions are worth 4-6 marks and this particular question is worth 10 so I feel like there must be more to it. Any help is greatly appreciated.