Reactive Extensions meant specifically for implementations of IObservable<bool>.
$ dotnet add package Reactive.BooleanReactive Extensions meant specifically for implementations of IObservable<bool>
This documentation uses marble diagrams to explain the transformations of IObservable<bool>. More on marble diagrams can be found in the documentation of ReactiveX.
Article containing examples in relation to home automation: Article with examples.
This library has extension methods for logical operators.
All operators except for Not are implemented using CombineLatest. This means that the first output is only emitted if all inputs have emitted an value after subscribing. For this reason, it makes sense to apply logical operators to stateful observables. In this context these are observables that emit their current state the moment an observer subscribes to them. This can easily be achieved by using Prepend, preferably in combination with Observable.Defer. For example:
Observable.Defer(() => source.Prepend(initialState));
Depending on the operator, there are several ways of handling value distinctness. Different forms are explained below.
Returns an observable in which the input is inverted.

Returns an observable that combines the latest of the provided observables using an AND operator.
The And method accepts three values to determine distinctness of the output:
OutputDistinctUntilChanged (default)
DistinctUntilChanged is applied to the returned observable, meaning a "true" can only be followed by a "false" and vice versa.

InputDistinctUntilChanged
DistinctUntilChanged is applied to the inputs only. Meaning that consecutive values on the input do not change the output, but input changes on different inputs can. For example, going from "false", "false" to "true", "false" will emit consecutive "false" values.
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NotDistinct
DistinctUntilChanged is never applied. Meaning both consecutive input and output values will be emitted.
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Returns an observable that combines the latest of the provided observables using an OR operator.
The Or method accepts three values to determine distinctness of the output:
OutputDistinctUntilChanged (default)
DistinctUntilChanged is applied to the returned observable, meaning a "true" can only be followed by a "false" and vice versa.

InputDistinctUntilChanged
DistinctUntilChanged is applied to the inputs only. Meaning that consecutive values on the input do not change the output, but input changes on different inputs can. For example, going from "true", "false" to "true", "true" will emit consecutive "true" values.
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NotDistinct
DistinctUntilChanged is never applied. Meaning both consecutive input and output values will be emitted.
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Returns an observable that combines the latest results of two observables using an XOR operator.
As changing distinct inputs will always result in a distinct XOR output, the Xor method accepts only two values to determine distinctness of the output:
distinctUntilChanged = true (default)
DistinctUntilChanged is applied to the result.

distinctUntilChanged = false
DistinctUntilChanged is not applied to the result.
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This library also implements inverted operators Nand, Nor and Xnor.
This library also has extension methods for scheduling:
Returns an observable that won't emit false for at least timespan after an initial "true" is emitted by source.

Example Use Case
Turn on a light for at least 3 seconds after a button was pressed. If 3 seconds are passed, only keep it on if the button is still being pressed, but immediately turn if off if not.
// buttonPressed is a IObservable<bool>
var buttonPressed = button.StateChanges().Select(s => s.State == "pressed");
buttonPressed
.TrueForAtLeast(TimeSpan.FromSeconds(3), scheduler)
.SubscribeTrueFalse(
() => light.TurnOn(),
() => light.TurnOff());Returns an observable that stays true for a time span once the source observable turns back to false.

Example Use Case
Keep a light on for 3 more seconds after last motion was detected.
// motionDetected is a IObservable<bool>
var motionDetected = motionSensor.StateChanges().Select(s => s.State == "motion detected");
motionDetected
.PersistTrueFor(TimeSpan.FromSeconds(3), scheduler)
.SubscribeTrueFalse(
() => light.TurnOn(),
() => light.TurnOff());Returns an observable that emits true once the source observable emits true for a minimum time span.

Example Use Case
Send notification when washing machine power has been 0 for at least 1 minute.
// washingMachineCurrentIsZero is a IObservable<bool>
var washingMachineCurrentIsZero = washingMachineCurrent.StateChanges().Select(s => s.State == 0);
washingMachineCurrentIsZero
.WhenTrueFor(TimeSpan.FromMinutes(1), scheduler)
.SubscribeTrue(() => notification.Send("Washing machine is done!"));Returns an observable that stays true for a maximum of time span. If the source observable emits false before the time has passed, the resulting observable also emits false.

Example Use Case
Keep closet lights on for a maximum amount of time.
// closetDoorOpen is a IObservable<bool>
var closetDoorOpen = closetDoor.StateChanges().Select(s => s.State == "open");
closetDoorOpen
.LimitTrueDuration(TimeSpan.FromMinutes(2), scheduler)
.SubscribeTrueFalse(
() => closetLight.TurnOn(),
() => closetLight.TurnOff());Besides transformations, this library has extension methods that help with common cases of subscribing to implementations of IObservable<bool>: SubscribeTrueFalse, SubscribeFalse and SubscribeTrue.
boolObservable.SubscribeTrueFalse(
() => {
// Logic for when observable emits true.
},
() => {
// Logic for when observable emits false.
}
)