Given that everything that is, is, something cannot both be true and false at the same time under the same circumstances. Either A or not A. Either I am married or I am unmarried. Either I am alive, or dead.
This idea forms the second and third laws of thought: noncontradiction and the excluded middle.
Identity says that everything is itself; whatever is, is. Noncontradiction says that it is itself and not something else; whatever is, cannot not be. The law of the excluded middle says that no third way is possible; everything either is or is not.
The rules include things that are mutually exclusive of one another, but not do not include either/or statements that admit other possibilities.
For example, I have a glass of something to drink. It is either water or something else. Water or not water. I can say that about any liquid: this liquid, or not this liquid. But under the LNC, I cannot say "it is water or milk." I may be able to make that assertion if someone poured a drink for me and the only drinkable liquids in my house are water and milk. In that case, I have eliminated all other possibilities. However, it does not follow from the LNC that my drink is either water or milk. Water and milk do not logically contradict.
To attempt to say logically that my drink is either milk or water is to commit the fallacy of the excluded middle, i.e. to say that there is no third way when there actually is.