Logic Theorems

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These are from my electronics textbook, I think it would be a cool exercise to fill these in.

Legend:
* the AND operator
+ the OR operator
X, Y, Z... variables
= implies
1 true
0 false
- NOT

THEOREMS

I am terrifyingly reminded of a mini course in computing that was obligatory at university at some point ( circa 1982/3) which i didn't understand AT ALL. More frighteningly alien to me than chinese.
I'm looking forward to seeing some answers so that i can get some idea about what is actually supposed to be done with this stuff. I can remember when Maths A-level ( age 16-18 ), went higher algebraic on me and how it was like when trying to learn french at age 11 and i didn't get that " il" meant "he" or "it", because i didn't even know what part of language "il" was.

I find symbolic logic to be quite fun.

Actually, we've had them presented like this:

AND = ^
OR = v
IMPLIES = -->
T = True
F= False
NOT = ~

And some additional ones:

EQUIVALENT <-->

So X+ 0 = X translates to X vY --> X; Y is always F. So if X is T, then TvF-->T. If X is F, then FvF-->F. And so on.

There are some other important tautologies:

[X-->Y ^X] --> Y Modus Ponens
[X-->Y^~Y]-->~X Modus Tollens
[X-->Y^Y-->Z]-->[X-->Z] Hypothetical Syllogism

For those less familiar with symbollic logic, here is a guide:

AND
X^Y
T if both X and Y are T. F otherwise.

OR
XvY
F if both X and Y are F. T otherwise.

IMPLIES
X-->Y
F if X is T and Y is F. T otherwise. (this is an important one. It's commonly mistaken for the equivalent argument.)

EQUIVALENT
X <--> Y
T if X and Y are both the same. F otherwise.

NOT
~X
T if X is F, and F is X is T.

Symbolic logic was one of my favorite Philosophy classes because it was the only one where I could get correct answers. Also, the prof. told us that as long as we submitted all the assignments, we didn't have to come to class. I even continued doing symbolic logic for a while after college because it put my mind in such a peaceful state. Great stuff!