This is a logical statement.
The enemy of my enemy is my friend. -True; because it is said to be.
The friend of my enemy is my enemy. -Not a logical conclusion.
If I have no enemy, I have no friends. -Given the statement, this could be true; but it might not be.
In general you are dealing with any number of logical statements, and there is a very discrete and mathematical way of handling it. What you see above is not that; its just a conceptualization - trust me, the math is in latin and all types of logical mathematical symbols.
There is no point to knowing this, unless you want to know how Artifical Intelligence works, or various types of mathematics... or; just for fun...
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