Logical operators (&, |, ~) in MATLAB - Mini Project: Build & Apply

Logical Operators (&, |, ~) in MATLAB

📖 Scenario: You are working with a simple security system that checks multiple conditions to decide if access should be granted.

🎯 Goal: Build a MATLAB script that uses logical operators & (AND), | (OR), and ~ (NOT) to evaluate access conditions.

📋 What You'll Learn

Create logical variables representing conditions

Use logical AND & to combine conditions

Use logical OR | to combine conditions

Use logical NOT ~ to invert a condition

Display the final access decision

💡 Why This Matters

🌍 Real World

Logical operators are used in security systems, decision making, and filtering data based on multiple conditions.

💼 Career

Understanding logical operators is essential for programming, data analysis, and automation tasks in many technical jobs.

1

Create initial logical variables

Create three logical variables in MATLAB: hasKey set to true, knowsPassword set to false, and isAdmin set to true.

MATLAB

% Your code here to create logical variables hasKey, knowsPassword, and isAdmin

Hint

Use true and false to assign logical values in MATLAB.

2

Add a condition variable for access by key and password

Create a new logical variable called accessByKeyAndPassword that is true only if both hasKey and knowsPassword are true using the logical AND operator &.

MATLAB

hasKey = true;
knowsPassword = false;
isAdmin = true;
% Your code here to create accessByKeyAndPassword using &

Hint

Use & to combine two logical variables for AND.

3

Create a condition for access by key or admin

Create a logical variable called accessByKeyOrAdmin that is true if either hasKey or isAdmin is true using the logical OR operator |.

MATLAB

hasKey = true;
knowsPassword = false;
isAdmin = true;
accessByKeyAndPassword = hasKey & knowsPassword;
% Your code here to create accessByKeyOrAdmin using |

Hint

Use | to combine two logical variables for OR.

4

Display the final access decision using NOT operator

Create a logical variable called noAccess that is the opposite of accessByKeyOrAdmin using the logical NOT operator ~. Then display noAccess using disp.

MATLAB

hasKey = true;
knowsPassword = false;
isAdmin = true;
accessByKeyAndPassword = hasKey & knowsPassword;
accessByKeyOrAdmin = hasKey | isAdmin;
% Your code here to create noAccess using ~ and display it

Hint

Use ~ to invert a logical variable and disp to show the result.

Practice

1. Which logical operator in MATLAB returns true only if both conditions are true?

easy

A. ~ (NOT)

B. & (AND)

C. | (OR)

D. ^ (XOR)

Solution

1. Step 1: Understand the AND operator

   The & operator returns true only when both conditions it compares are true.

2. Step 2: Compare with other operators

   The | operator returns true if at least one condition is true, ~ negates a condition, and ^ is XOR which returns true if exactly one condition is true.

3. Final Answer:

   & (AND) -> Option B

4. Quick Check:

   Both true = true means AND = & [OK]

Hint: AND means both true, use & operator [OK]

Common Mistakes:

• Confusing & with | operator
• Thinking ~ returns true if both true
• Mixing XOR (^) with AND (&)

2. Which of the following is the correct syntax to negate a logical variable a in MATLAB?

easy

A. not a

B. !a

C. ~a

D. a~

Solution

1. Step 1: Recall MATLAB negation syntax

   In MATLAB, the negation operator is ~ placed before the variable to flip its logical value.

2. Step 2: Check each option

   not a uses 'not' which is not valid syntax, C uses '!' which is not MATLAB syntax, and D places '~' after the variable which is incorrect.

3. Final Answer:

   ~a -> Option C

4. Quick Check:

   Negate with ~ before variable [OK]

Hint: Use ~ before variable to negate in MATLAB [OK]

Common Mistakes:

• Using ! instead of ~ for negation
• Writing negation after variable
• Using 'not' keyword which is invalid

3. What is the output of the following MATLAB code?

a = true; b = false; c = a & ~b;

medium

A. true

B. false

C. 1

D. 0

Solution

1. Step 1: Evaluate ~b

   Since b is false, ~b is true.

2. Step 2: Evaluate a & ~b

   Both a and ~b are true, so a & ~b is true.

3. Final Answer:

   true -> Option A

4. Quick Check:

   true AND true = true [OK]

Hint: Negate false to true, then AND with true gives true [OK]

Common Mistakes:

• Confusing logical true/false with numeric 1/0
• Forgetting to negate b
• Assuming & acts like | (OR)

4. Identify the error in this MATLAB code snippet:

a = true;
b = false;
c = a | ~ b;

medium

A. No error, code runs correctly

B. Incorrect use of | operator

C. Extra space between ~ and b causes error

D. Missing parentheses around ~b

Solution

1. Step 1: Check operator usage

   The | operator is correctly used to perform logical OR between a and ~b.

2. Step 2: Check negation syntax

   The negation operator ~ can have a space before the variable; MATLAB ignores spaces here.

3. Final Answer:

   No error, code runs correctly -> Option A

4. Quick Check:

   Logical OR with negation syntax is valid [OK]

Hint: Spaces around ~ do not cause errors in MATLAB [OK]

Common Mistakes:

• Thinking ~ needs parentheses always
• Assuming space causes syntax error
• Confusing | with & operator

5. Given logical variables x = [true false true] and y = [false true true], what is the result of z = ~(x & y) | (x | y) in MATLAB?

hard

A. [false false false]

B. [false true true]

C. [true false true]

D. [true true true]

Solution

1. Step 1: Calculate x & y element-wise

   x = [true false true], y = [false true true]
   x & y = [true & false, false & true, true & true] = [false, false, true]

2. Step 2: Negate x & y

   ~(x & y) = [~false, ~false, ~true] = [true, true, false]

3. Step 3: Calculate x | y element-wise

   x | y = [true | false, false | true, true | true] = [true, true, true]

4. Step 4: Calculate final expression

   z = ~(x & y) | (x | y) = [true | true, true | true, false | true] = [true, true, true]

5. Final Answer:

   [true true true] -> Option D

6. Quick Check:

   Element-wise logic with ~, &, | gives all true [OK]

Hint: Calculate & first, then ~, then | element-wise [OK]

Common Mistakes:

• Forgetting element-wise operation
• Negating before AND instead of after
• Mixing up & and | precedence