Recognizing Boolean expressions that simplify is valuable while programming and on the AP CS A Exam. An expression that always evaluates to `true`

or always evaluates to `false`

is likely a logical error. Similarly, an expression that includes an irrelevant part is likely an error.

Identifying equivalent Boolean expressions is often tested on the AP CS A Exam multiple choice. The question is often phrased as “Which of the following is equivalent to … ?”

The exercises below are presented without multiple choice options. Each expression simplifies in some way, which is not always the case with Boolean expressions on the AP CS A Exam. Answers and explanations are available individually (linked with each exercise) and as a single page (linked at the end).

The expressions below imply the types of the variables. Problems on the AP CS A Exam typically explicitly specify types.

Simplify each expression, except when otherwise noted.

## Exercise 1

Distribute the not.

```
!(a && b && c)
```

## Exercise 2

```
(a && b) && !(a && b)
```

## Exercise 3

```
!((x < y) && (r >= s))
```

## Exercise 4

```
(x > y) || (x <= y)
```

## Exercise 5

```
(a && b) && (!a || !b)
```

## Exercise 6

```
(a || b) && a
```

## Exercise 7

```
(a && b) || b
```

## Exercise 8

```
(a && b) || (a && b)
```

## Exercise 9

```
(a || b) || a
```

## Exercise 10

```
(a || b) || !(a || b)
```

## Exercise 11

```
!((x < y) || (q > r))
```

## Exercise 12

```
(a || b) && (!a && !b)
```

## Exercise 13

Tell when the expression evaluates to `true`

.

```
!(a || b)
```

## Exercise 14

Tell when the expression evaluates to `true`

.

```
(a || b) && (!a || !b)
```

## Solutions & comments

See the Boolean expression simplification solutions or review them with AP CS Tutor Brandon Horn.