Logical Operators Examples: 47 Problems with Answers

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Logical Operators.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in CS Thinking.

Concept Recap

Operators that combine or modify boolean expressions: AND (true only when both operands are true), OR (true when at least one operand is true), and NOT (reverses a boolean value from true to false or vice versa).

AND is strict (both must be true), OR is flexible (either works), NOT flips the result.

Read the full concept explanation →

How to Use These Examples

Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Logical operators let you build complex conditions from simple boolean tests.

Common stuck point: AND requires ALL conditions true; OR only requires ONE — easy to confuse.

Sense of Study hint: When combining conditions with AND/OR, evaluate each condition separately first, then combine. Remember: AND narrows results (both must be true), OR broadens results (either suffices). Use parentheses to make the order of evaluation explicit.

Worked Examples

Example 1

medium

Evaluate

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

for

A=

True,

B=

True,

C=

False, using standard precedence.

Answer

False

First step

NOT B = NOT True = False.

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Example 2

medium

Use De Morgan to rewrite:

\text{NOT}(x > 0 \text{ OR } y > 0)

Example 3

medium

Identify the bug: `if (x = 0 OR 1 OR 2)` is meant to test whether x is 0, 1, or 2.

Example 4

hard

Simplify

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

using boolean algebra.

Example 5

hard

Simplify the condition: `NOT (age < 13 OR age > 65)`.

Example 6

challenge

A condition `(NOT a) OR (NOT b)` is being optimized. Show two equivalent simpler forms.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy

Evaluate:

\text{True AND False}

AND truth table — highlighted row shows True AND False.

Example 2

easy

Evaluate:

\text{True OR False}

OR truth table — highlighted row shows True OR False.

Example 3

easy

Evaluate:

\text{NOT True}

Example 4

easy

Evaluate:

\text{True XOR True}

(XOR is true when operands differ).

XOR truth table — highlighted row shows True XOR True.

Example 5

easy

Evaluate:

\text{False OR False}

OR truth table — highlighted row shows False OR False.

Example 6

easy

Evaluate:

\text{True AND True}

AND truth table — highlighted row shows True AND True.

Example 7

easy

Evaluate:

\text{NOT (False)}

Example 8

easy

In `x == 5 OR 10`, why is this a logic bug when checking if x is 5 or 10?

Example 9

medium

Evaluate

\text{NOT True AND False}

using precedence (NOT before AND).

Evaluating NOT True AND False step by step (NOT binds first).

Example 10

medium

Evaluate

\text{True OR False AND False}

using precedence (AND before OR).

Evaluating True OR False AND False step by step (AND binds first).

Example 11

medium

Using De Morgan's law, rewrite

\text{NOT (A AND B)}

without the outer NOT.

Example 12

medium

Using De Morgan's law, rewrite

\text{NOT (A OR B)}

without the outer NOT.

Example 13

medium

A short-circuit AND `A AND B` skips evaluating B when A is false. If A is `False`, is B evaluated?

Example 14

medium

Evaluate

(\text{True AND False}) \text{ OR } (\text{NOT False})

Evaluating (True AND False) OR (NOT False) in three steps.

Example 15

medium

For a discount, a customer needs (age over 65) OR (student AND member). If age=70, student=False, member=False, does the customer qualify?

Discount condition: (age > 65) OR (student AND member) with age=70, student=False, member=False.

Example 16

challenge

Simplify

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

using De Morgan and double negation.

Example 17

challenge

XOR can be built from AND, OR, NOT. Verify that

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

for

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

Example 18

challenge

A condition `NOT (x > 0 AND x < 10)` should reject values inside (0,10). Rewrite it with De Morgan into an OR of comparisons.

Example 19

medium

Evaluate

\text{NOT (True OR False) AND True}

using precedence.

Example 20

medium

Access is granted if `(isAdmin OR isOwner) AND NOT isBanned`. For isAdmin=False, isOwner=True, isBanned=False, is access granted?

(isAdmin OR isOwner) AND NOT isBanned with isAdmin=F, isOwner=T, isBanned=F.

Example 21

easy

Evaluate:

\text{False AND True}

AND truth table — highlighted row shows False AND True.

Example 22

easy

Evaluate:

\text{False OR True}

OR truth table — highlighted row shows False OR True.

Example 23

easy

Evaluate:

\text{True XOR False}

(XOR is true when operands differ).

XOR truth table — highlighted row shows True XOR False.

Example 24

easy

How many rows does the truth table for

A

AND

B

have?

Complete truth table for A AND B — count the rows to answer the question.

Example 25

easy

Which operator binds TIGHTEST (highest precedence): AND, OR, or NOT?

Example 26

easy

Evaluate:

\text{True AND True AND False}

Evaluating True AND True AND False left to right.

Example 27

medium

Evaluate

\text{NOT(True AND False) OR False}

using precedence.

Evaluating NOT(True AND False) OR False in three steps.

Example 28

medium

Rewrite

\text{NOT}(x = 5)

without NOT, using a comparison.

Example 29

medium

A discount is given if (member AND age >= 18) OR (employee). Are member=False, age=25, employee=True eligible?

(member AND age >= 18) OR employee with member=F, age=25, employee=T.

Example 30

medium

Short-circuit OR: in `A OR B`, B is skipped if A is True. If A=True and B is `1/0`, does the expression crash?

Example 31

medium

Evaluate

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

for

A=

True,

B=

False.

Example 32

medium

The expression

A \text{ AND NOT } A

is what kind of formula?

Example 33

medium

Access if `loggedIn AND (isAdmin OR isOwner)`. For loggedIn=True, isAdmin=False, isOwner=False, is access granted?

loggedIn AND (isAdmin OR isOwner) with loggedIn=T, isAdmin=F, isOwner=F.

Example 34

medium

If short-circuit AND is used and `A AND B` evaluates only A when A is False, what design rule does this enable?

Example 35

hard

Simplify

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

using boolean algebra.

Example 36

hard

Show that

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

by testing

(A,B) = (\text{T},\text{F})

Example 37

hard

Three variables

A, B, C

. Build a truth-table expression that is True only when EXACTLY one of them is true.

Example 38

hard

Why is `{NAND}` (NOT AND) considered functionally complete on its own?

Example 39

hard

Simplify:

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

Example 40

challenge

A short-circuit AND in `expensiveCheck() AND cheapCheck()` runs the expensive one first. What is the smell, and the fix?

Example 41

challenge

Write the negation of 'every student passed' using logical operators (formally).

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Related Concepts

Boolean Logic Selection Truth Tables Boolean

Background Knowledge

These ideas may be useful before you work through the harder examples.

boolean logicselection