Express each of these statements using quantifiers. Then form the negation of the statement so that no negation is to the left of a quantifier. Next, express the negation in simple English. (Do not simply use the phrase “It is not the case that.”)
- No one has lost more than one thousand dollars playing the lottery.
- There is a student in this class who has chatted with exactly one other student.
- No student in this class has sent e-mail to exactly two other students in this class.
- Some student has solved every exercise in this book.
- No student has solved at least one exercise in every section of this book.