## Translating English to Symbolic Logic

The following is the list of problems for Section 2.9 of the Book of Proof (page 57). There is a forum open at the end, so you can ask questions. It is a great way to interact with the instructor and with other students in your class, should you need some assistance with any question. Please, do not post solutions.

Translate each of the following sentences into symbolic logic.

1. If $$f$$ is a polynomial and its degree is greater than 2, then $$f’$$ is not constant.
2. The number $$x$$ is positive but the number $$y$$ is not positive.
3. If $$x$$ is prime then $$\sqrt{x}$$ is not a rational number.
4. For every prime number $$p$$ there is another prime number $$q$$ with $$q > p$$.
5. For every positive number $$\varepsilon$$, there is a positive number $$\delta$$ for which $$\lvert x - \alpha \rvert < \delta$$ implies $$\lvert f(x) - f(\alpha) \rvert < \varepsilon$$.
6. For every positive number $$\varepsilon$$ there is a positive number $$M$$ for which $$\lvert f(x) - b \rvert < \varepsilon$$, whenever $$x > M$$.
7. There exists a real number $$a$$ for which $$a + x = x$$ for every real number $$x$$.
8. I don’t eat anything that has a face.
9. If $$x$$ is a rational number and $$x \neq 0$$ then $$\tan(x)$$ is not a rational number.
10. If $$\sin(x) < 0$$, then it is not the case that $$0 \leq x \leq \pi$$.
11. There is a Providence that protects idiots, drunkards, children and the United States of America. (Otto von Bismark)
12. You can fool some of the people all of the time, and you can fool all of the people some of the time, but you can’t fool all of the people all of the time. (Abraham Lincoln)
13. Everything is funny as long as it is happening to somebody else. (Will Rogers)