- #1
Mr Davis 97
- 1,462
- 44
Homework Statement
Homework Equations
The Attempt at a Solution
1) There exists a grey cat.
Negation: Every cat is not grey.
2) For all cats there exists an owner.
Negation: There exists a cat without an owner.
3) There exists a grey cat for all owners.
Negation: There exists an owner that can't own a grey cat.
4) Every fire engine is red and every ambulance is white.
Negation: There exists a fire engine that isn't red or there exists an ambulance that isn't white.
5) Some of the students in the class are not here today.
Negation: Every student is in class today.
6) Let ##x,y,z \in \mathbb{Z}##. For all x there exists a y such that ##x=y+z##.
Negation: Let ##x,y,z \in \mathbb{Z}##. There exists an x such that for all y, ##x \ne y+z##.
7) There exists unique x such that P(x) us true.
Negation: If x satisfies P(x) then there is a y distinct from x which does too.
8) All mathematics students are hardworking.
Negation: There exists a mathematics student who is lazy.
9) Only some of the students of the class are here today.
Negation: Every student is not in class today.
10) The number ##\sqrt{x}## is rational if ##x## is an integer.
Negation: There exists an integer ##x## such that ##\sqrt{x}## is irrational.I know that this is quite a bit, but I want to make sure that I have negation down.