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Anarchism = (((an + arche)ist)ism)

This equation makes no logical or mathematical sense, "an-" is an operation of subtraction, annulling, annihilating:
Anarchy = arche - arche = 0, Anarchy= 0

But just as some infinities are bigger than others, some zeros are bigger than others:
Nihilism = everything - everything = 0, Nihilism= 0

If anarchy is the event of this annulling of arche, and arche and anarchy are mutually exclusive events, they can be expressed by using the complement rule in probability. q = 1 − p
P(Anarchy) = 1 – P(Arche), or P(Arche) = 1 – P(Anarchy), or 1 = P(Anarchy) + P(Arche)

Since we know for a fact that arche exists, then that would mean that the probability of anarchy existing would be zero, and the probability of arche existing would be 1. That would mean arche is a certain event, while anarchy is an impossible event.
Expressed as propositional equivalences, that would make arche a tautology, and anarchy, a contradiction.
A tautology is a proposition that is always true. Example 2.1.1. p ∨¬p
A contradiction is a proposition that is always false. Example 2.1.2. p ∧¬p

That is assuming they're mutually exclusive events. Not all mutually exclusive events are commonly exhaustive.

If anarchy as an event is dependent on arche ocurring, then the conditional probability would be expressed as:
Conditional Probability of Anarchy given Arche: P (Anarchy|Arche) = P(Anarchy ∩ Arche)⁄P(Arche)

If anarchy and arche are independent events, we can't know the probability of anarchy if we know the probability of arche:
P Anarchy ∩ Arche = P Arche .P Anarchy

Both could occur at the same time, as well as at different times, and you could draw a venn diagram of the times they coincide and don't.

In this case, anarchy expressed as a propositional equivalency would be a contingency. A contingency is a proposition that is neither a tautology nor a contradiction. Example 2.1.3. p ∨q →¬r

References:
- How to Prove the Complement Rule in Probability, https://www.thoughtco.com/prove-the-complement-rule-3126554
- Binomial distribution, https://en.wikipedia.org/wiki/Binomial_distribution
- Propositional Equivalences, https://www.math.fsu.edu/~pkirby/mad2104/SlideShow/s2_2.pdf
- Propositional Logic: Syntax, https://www.cs.cornell.edu/courses/cs280/2008sp/280wk12_x4.pdf
- Musings on Nothingness (And some of its varieties), https://theanarchistlibrary.org/library/baedan-musings-on-nothingness