The two most fundamental rules of logic are the Law of Noncontradiction and the Law of Transitive Properties. In fact, all of the other rules of logic stem from these two laws. Both laws are very simple and easy to understand, yet people frequently ignore or misuse them. Therefore I will attempt to explain how they actually work.
Law of Noncontradiction
This law simply states that something cannot be A and not A simultaneously. In other words, two mutually exclusive things cannot exist at the same time. So, for example, the Law of Noncontradiction tells us that it is impossible for both an immovable object and an unstoppable force to exist simultaneously, because each one cancels the other out. In other words, if there is an object that is truly immovable, then there cannot be an unstoppable force because this would contradict the properties of the immovable object. Conversely, if…
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Utopia, you are standing in it! 
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