Truth tables are really simple when we understand the concept. Imagine T and F as a binary value like 1 and 0. There are just two possible states true or false (1 or 0). So truth tables try to demonstrate the possible combination betwen this values.
So to do this combinations truth tables uses some kinds of operations but here I'll explain just the principals for you and the operations are "and" and "or".
How this operations works?
It's simple, for the operation "and", when we try to combine two possible states (the values we explained before), the result must also be one of the states. Bellow I draw the operation and to ilustrate.
We can see above that using the operation "and" we always get 0 unless we have a 1 AND a 1 together. That means when we have a false value in the operation, so the result is false.
Now let's see how the "or" operation works (remember that "or" also is represented by V simbol).
So, here We have the contrary. When using the operation "or" always we have a True value, the result is True.
Now there is anothe operation represented by this simbol ~. This operation we can call, "NON somethins". So Aways we have a ~ before state, so we represent it by the opposite like is represented bellow.
So, for your truth table we can say we have two different variables (p,q) and both are that king of variable that can be represented just as 1 or 0 which means True or False which means Tor F. So we can display all the possible combinations betwen "p" and "q" and also we will display the values for ~p.
That is what we do.
