Enigma'07 said:
I have no clue what you are talking about.
What level of math?
It's just basic logic. I'll try and walk you through it.
So we start out with our statement, A or ~A.
For this statement to be true, either A or not A must be true, which is just how the logical or operator works.
So to create a truth table we generate a table with all the possible truth values for our variables. Since we only have one and our we have binary truths, we only have 2 values (true and false).
So we start with this:
A | A or ~A
------------
T
F
Now we apply those values to the statement. The controlling operator is the or. So to find the actual truth we need to figure out whether or not the or is true. The only other operator is the not. So first we figure out the values for the not (~).
A | A or ~A
------------
T | | | F
F | | | T
Now that that's done since we already know the value of A from the our left table we can assign a value to the or, knowing that for an or to be true only one of its members needs be true. So....
A | A or ~A
------------
T | | T | F
F | | T | T
And we have a finished truth table for (A or ~A). To be a tautology every statement must be true. Since this table meets that criteria, the premise is a tautology.
No matter what we put into the this phrase it will be true.
Examples:
It is raining here or it is not raining here.
I am a man or I am not a man.
There is a god or there is not a god.
In any event. I hope this helped some.