Practice Truth Tables in CS Thinking

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

A table listing every combination of boolean inputs and the resulting output for a logical expression.

Map out every possible True/False scenario to be sure you understand what a logical expression does.

Showing a random 20 of 50 problems.

Example 1

hard

Are

A \text{ AND (B OR C)}

and

(A \text{ AND } B) \text{ OR } (A \text{ AND } C)

equivalent? Justify on all 8 rows.

Example 2

medium

In a 3-variable truth table, how many rows have at least one variable False?

Example 3

medium

Build the truth table for

\text{NOT } A \text{ OR } B

. For which of the 4 (A,B) rows is it False?

Which row of NOT A OR B is False?

Example 4

easy

In the truth table for

A \text{ XOR } B

, how many of the 4 rows are True?

Truth table for A XOR B — exactly 2 of 4 rows are True

Example 5

medium

Does

A \text{ OR (A AND B)}

simplify to

A

? Check with the truth table.

Absorption law: A OR (A AND B) matches A on all 4 rows

Example 6

hard

An expression on

A,B

outputs True on rows

(T,T)

and

(F,F)

, False elsewhere. Write a simple AND/OR/NOT expression matching it.

Build the expression that matches this truth table (XNOR pattern)

Example 7

hard

How many distinct boolean functions exist on

3

variables? Justify the count.

Example 8

medium

A truth table for an expression in 5 variables would have how many rows, and why is exhaustive checking still feasible by computer?

Example 9

medium

How many True rows does the truth table for

A \text{ AND } B \text{ AND } C

have?

A AND B AND C — only 1 of 8 rows is True

Example 10

easy

How many rows does a truth table for

5

boolean variables have?

Example 11

easy

How many rows does a truth table for 4 boolean variables have?

Example 12

hard

Use a truth table to test whether

A \text{ AND (NOT } A \text{ OR } B)

simplifies to

A \text{ AND } B

Example 13

medium

Use a truth table to decide whether

A \text{ XOR } A

is equivalent to False (a contradiction).

A XOR A is always False — a contradiction

Example 14

medium

Evaluate

\text{NOT}(A \text{ OR } B)

when

A=\text{False}, B=\text{False}

Evaluate NOT(A OR B) when A=False, B=False

Example 15

challenge

Verify with truth tables that NAND alone is functionally complete by expressing NOT, AND, and OR using only NAND.

Example 16

challenge

A 3-input majority function MAJ

(A,B,C)

outputs True when at least two inputs are True. How many True rows does its truth table have, and write it in DNF.

Example 17

easy

In the truth table for

A \text{ OR } B

, how many of the 4 rows are True?

Truth table for A OR B — 3 of 4 rows are True

Example 18

medium

Verify whether

A \text{ AND (A OR B)}

is equivalent to

A

using all 4 rows.

Absorption law: A AND (A OR B) equals A on all 4 rows

Example 19

easy

For

A=\text{False}, B=\text{True}

, what is

A \text{ XOR } B

Read off: A=False, B=True gives A XOR B = True

Example 20

challenge

How many distinct truth tables (boolean functions) exist for 2 input variables, and why?

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Related Concepts

Boolean Logic Logical Operators