A little confused on some geometry questions?

Question

Which of the following statements is the best example of a theorem?

Martians come from the planet Mars.

Most car accidents happen at night.

A line is an infinite set of points that extends in opposite directions.

All fish can swim.

I think it would all fish can swim because that's been proven and that's what a theorem is.

A proof may contain which of the following?

only definitions

only postulates

only theorems

all of the above

I think this one would be all of the above because all of these could be used as proof.

Am I understanding these right?

Answer 1

I agree with your answers.

In the first question, the items about Martians and lines are definitions rather than theorems, and the one about accidents is a statistic.

You've got the best response on the second, although it's incorrectly worded, since "all of the above" would logically include the repetitions of the word "only" and that word is inappropriate to include.

By "best response" in this case I mean that even though the writer mis-stated the question, that's the answer the writer clearly intended.