# J Appendix J: Chapter 10 Exercise Solutions Written by Massimo Carli

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## Exercise 10.1

What’s the cardinality of the following type?

``````typealias Triplet = Triple<UByte, Boolean, Unit>
``````

### Exercise 10.1 solution

As you learned in the chapter, the cardinality of `Triplet` is the product of the cardinalities of `UByte`, `Boolean` and `Unit`, which are:

``````UByte * Boolean * Unit = 256 * 2 * 1 = 512
``````

## Exercise 10.2

What’s the cardinality of the following type?

``````typealias Unique = Pair<Unit, Unit>
``````

### Exercise 10.2 solution

Of course, the cardinality of `Unique` is exactly `1` because `Unit` is the only existing value of type `Unit`. Because of this, `Unique` is isomorphic to `Unit`.

## Exercise 10.3

What’s the cardinality of the following type?

``````typealias MultiEither = Either<UByte, Either<Boolean, Triage>>
``````
``````typealias MultiEither2 = Either<Either<UByte, Boolean>, Triage>
``````

### Exercise 10.3 solution

In the chapter, you learned that `Either<A, B>` is a way to represent addition. For this reason, you can represent the previous definition like:

``````UByte + (Boolean + Triage) = 256 + (2 + 3) = 256 + 5 = 261
``````
``````(UByte + Boolean) + Triage = (256 + 2) + 3 = 256 + 5 = 261
``````

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