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

P

T

F

If we add another statement Q, there are now 4 possibilites, both true, P true Q false, vice versa, or both false:

P Q

T T

T F

F T

F F

Wikipedia 'Truth tables' for more examples, and usage of the AND, OR, NOT statements.

Hope this helps!