#
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
```