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 1 solution

Exercise 2

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

Exercise 2 solution

Exercise 3

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

Exercise 3 solution

Exercise 4

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

Exercise 4 solution

Exercise 5

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

Exercise 5 solution

Exercise 6

(a || b) && a

Exercise 6 solution

Exercise 7

(a && b) || b

Exercise 7 solution

Exercise 8

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

Exercise 8 solution

Exercise 9

(a || b) || a

Exercise 9 solution

Exercise 10

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

Exercise 10 solution

Exercise 11

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

Exercise 11 solution

Exercise 12

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

Exercise 12 solution

Exercise 13

Tell when the expression evaluates to true.

!(a || b)

Exercise 13 solution

Exercise 14

Tell when the expression evaluates to true.

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

Exercise 14 solution

Solutions & comments

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

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