Mutually exclusive in the context of "Embedded option"

A dichotomy (/daɪˈkɒtəmi/) is a partition of a whole (or a set) into two parts (subsets). In other words, this couple of parts must be

• jointly exhaustive: everything must belong to one part or the other, and
• mutually exclusive: nothing can belong simultaneously to both parts.

If there is a concept A, and it is split into parts B and not-B, then the parts form a dichotomy: they are mutually exclusive, since no part of B is contained in not-B and vice versa, and they are jointly exhaustive, since they cover all of A, and together again give A.

This article lists forms of government and political systems, which are not mutually exclusive, and often have much in common. According to Yale professor Juan José Linz there are three main types of political systems today: democracies, totalitarian regimes and, sitting between these two, authoritarian regimes with hybrid regimes. Another modern classification system includes monarchies as a standalone entity or as a hybrid system of the main three. Scholars generally refer to a dictatorship as either a form of authoritarianism or totalitarianism.

The ancient Greek philosopher Plato discusses in the Republic five types of regimes: aristocracy, timocracy, oligarchy, democracy, and tyranny. The question raised by Plato in the Republic: What kind of state is best? Generational changes informed by new political and cultural beliefs, technological progress, values and morality over millenniums have resulted in considerable shifts in the belief about the origination of political authority, who may participate in matters of state, how people might participate, the determination of what is just, and so forth.

Pursuit predation is a form of predation in which predators actively give chase to their prey, either solitarily or as a group. It is an alternate predation strategy to ambush predation — pursuit predators rely on superior speed, endurance and/or teamwork to seize the prey, while ambush predators use concealment, luring, exploiting of surroundings and the element of surprise to capture the prey. While the two patterns of predation are not mutually exclusive, morphological differences in an organism's body plan can create an evolutionary bias favoring either type of predation.

Pursuit predation is typically observed in carnivorous species within the kingdom Animalia, such as cheetahs, lions, wolves and early Homo species. The chase can be initiated either by the predator, or by the prey if it is alerted to a predator's presence and attempt to flee before the predator gets close. The chase ends either when the predator successfully catches up and tackles the prey, or when the predator abandons the attempt after the prey outruns it and escapes.

In probability theory, the complement of any event A is the event [not A], i.e. the event that A does not occur. The event A and its complement [not A] are mutually exclusive and exhaustive. Generally, there is only one event B such that A and B are both mutually exclusive and exhaustive; that event is the complement of A. The complement of an event A is usually denoted as A′, A, ${\displaystyle \neg }$A or A. Given an event, the event and its complementary event define a Bernoulli trial: did the event occur or not?

For example, if a typical coin is tossed and one assumes that it cannot land on its edge, then it can either land showing "heads" or "tails." Because these two outcomes are mutually exclusive (i.e. the coin cannot simultaneously show both heads and tails) and collectively exhaustive (i.e. there are no other possible outcomes not represented between these two), they are therefore each other's complements. This means that [heads] is logically equivalent to [not tails], and [tails] is equivalent to [not heads].