Seminar I

In the first lecture we looked at basic notions concerning the study of logic. The exercises below should refresh your memory about some of the issues raised in the lecture.

I. For the following statements, distinguish between object-language and meta-language:

1. The sentence `They feeds to cat' is ungrammatical in English.
2. The French translation of the English phrase `Thank you very much' is `Merci beaucoup'.
3. The equation $E = mc^2$ holds in special relativity
4. If $x^2 - 2x + 1 = 0$ then $x = 1$
5. If $x^2 - 2x + 1 = 0$ then $x$ must be unity.
6. `$E = mc^2$ holds in special relativity' cannot be proved
7. $x + 4 - 3 = x + 1$

II. Decide whether the following are declarative sentences or not:

1. What is you name?

2. Grass is red

3. Close the door!

4. He asked what your name is

5. You must not cheat

6. I command you to go

7. It is false that grass is red

III. Consider the following pairs of statements and decide whether they are contradictions or not.

1. It is raining. It is fine.
2. If it is raining, then it is wet. It is raining and it is dry.
3. If it is raining, then it is wet. It is fine and it is wet.
4. Either it is fine or it is wet. It is raining.

IV. Is the following argument correct?

If Francis Bacon had written Hamlet, then he'd have been a great writer. But Bacon didn't write Hamlet, so he was not a great writer.