A `boolean`

stores the result of a logical comparison and can take on one of two values:

Booleans were named after the nineteenth-century mathematician George Boole, who devised an arithmetic system based on the logic of true and false properties.

Booleans help us store a statement's truth or falsehood in a standard way. We evaluate true or false expressions everyday: "do I have my housekeys?" "Should I carry an umbrella?" "Have I called mom yet?"

Create a boolean by giving a boolean variable a true or false value:

```
boolean b = true;
boolean c = (5 < 4); // c is false
boolean e; // e doesn't yet have a value, but it's been initliazed
```

Two booleans are equal if they have the same value; that is, if they are both true or both false. For example:

```
true == true; // true
false == true; // false
false != true; // true
```

Suppose we have `int x = 4`

and `int y = 12`

. What can we say about the following statements?

```
boolean b = x > y;
// false, because 4 isn't larger than 12
boolean c = x == y;
// false, because 4 isn't equal to 12
boolean d = y > x;
// true, because 12 is greater than 4
```

Booleans can also be written with more complicated expressions:

```
boolean e = (20 - 10) > (9 * 1) // true
boolean f = (39 - 30) * 9 != 81 // false
```