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My professor, he's a good, witty guy. He wasn't satisfied with other textbooks, so he decided to write his own. Since it's not published yet, we get a free pdf version of it, downloadable.

Sadly, despite how good of a person he seems to be, he can't write a textbook for anything. It's very difficult to read without a dictionary and wikipedia at my side, and he fails to define many symbols and techniques, as well as providing zero examples or sample problems.

So, now that we have an assignment, I'm lost, naturally. I'm very capable of doing this assignment on my own, however I have absolutely no clue what they're asking, as he never defined what half of these symbols and words mean.

As such, I have a handful of small questions.

In advance, thank-you for any information given; you're helping save my education :)

1) [itex]A, A \rightarrow B \vdash B[/itex]- SOLVED -

I know what 'A' is, and I know what [itex]A \rightarrow B[/itex] is. But what does it mean when you have a list of variables to the left of a [itex]\vdash[/itex] symbol? What does [itex]\vdash[/itex] mean, and what does the entire phrase mean?

2) [tex]\frac{A, A \equiv B}{B}[/tex]- SOLVED -

Is this division? I think it has something to do with my first question, but again, I wouldn't have a clue. What does this fraction-like formation mean?

3) [itex]\vdash (A \rightarrow (B \rightarrow C))[/itex]- SOLVED -

Again, similar to my first question... if there is no list to the left of [itex]\vdash[/itex], what does this mean? It may not matter, but since I don't know the answer to the first question, I haven't a clue.

4) What's the difference betweent,f, T, and [itex]\perp[/itex]? In theory, t and T both mean true, but apparently there's some kind of difference, as I lost marks for this.- SOLVED -

5) What is the letter [itex]\Gamma[/itex] used for in this subject? It seems to be a set of formulae, or some kind of set, since my professor has been using [itex]\subset[/itex] and [itex]\subseteq[/itex] with it.- SOLVED -

6) [itex]T \equiv \perp \equiv \perp[/itex]- SOLVED -

I think this is saying that the statement "True = False" is false, but what does it mean when it has even more than two [itex]\equiv[/itex] signs, such as [itex]\perp \equiv \perp \equiv A \equiv A[/itex]? This likely has to do with hidden brackets, or my lack of understanding of the order of operations.

7) What is the difference between [itex]\vdash[/itex] and [itex]\models_{taut}[/itex]?- SOLVED -

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# Homework Help: Boolean Logic - Many simple questions

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