Your asking about Truth tables, just used to prove things in logic.
Basicly if we have a statement P, it is either True (T) or False (F)
so say P is x=5, then either x=5 (T), or x is not 5 (F)
We can summarise this in a table
If we add another statement Q, there are now 4 possibilites, both true, P true Q false, vice versa, or both false:
Wikipedia 'Truth tables' for more examples, and usage of the AND, OR, NOT statements.
Hope this helps!