Logical values in MATLAB

Introduction

Logical values help us decide if something is true or false, which is useful for making choices in programs.

Checking if a number is positive or negative.

Deciding whether to run a part of code based on a condition.

Filtering data to keep only certain values.

Testing if two values are equal or not.

Syntax

MATLAB

true  % represents logical true
false % represents logical false

% Logical expressions example:
a = 5;
b = 10;
result = (a < b); % result is logical true because 5 is less than 10

Logical values in MATLAB are either true (1) or false (0).

You can use logical values in if statements and loops to control program flow.

Examples

Assign logical true and false directly to variables.

MATLAB

x = true;
y = false;

Compare two numbers; isGreater will be true because 7 is greater than 3.

MATLAB

a = 7;
b = 3;
isGreater = (a > b);

Create a logical array where each element shows if the condition is true (greater than 3) or false.

MATLAB

vec = [1, 2, 3, 4, 5];
logicalVec = vec > 3;

Sample Program

We use logical values from the condition mod(number, 2) == 0 to decide which message to show.

MATLAB

% This program checks if a number is even or odd
number = 8;
if mod(number, 2) == 0
    disp('The number is even.')
else
    disp('The number is odd.')
end

Important Notes

Logical values are very useful for controlling which parts of your program run.

You can combine logical conditions using & (and), | (or), and ~ (not).

Logical arrays can help you select or change parts of data easily.

Summary

Logical values are either true or false and help make decisions in code.

You create logical values by comparing things or using true/false directly.

Use logical values in if statements and loops to control what your program does.

Practice

1. What is the result of the expression 5 > 3 in MATLAB?

easy

A. 5

B. false

C. 3

D. true

Solution

1. Step 1: Understand the comparison operator

   The operator > checks if the left number is greater than the right number.

2. Step 2: Compare the numbers 5 and 3

   Since 5 is greater than 3, the expression returns true.

3. Final Answer:

   true -> Option D

4. Quick Check:

   5 > 3 = true [OK]

Hint: Greater than means left number bigger than right [OK]

Common Mistakes:

• Confusing true with the number 5
• Thinking it returns the bigger number
• Mixing up > and < operators

2. Which of the following is the correct way to create a logical true value in MATLAB?

easy

A. 1 == 1

B. 1 = 1

C. logical(0)

D. true

Solution

1. Step 1: Evaluate each option

   logical(0) returns false.
   1 = 1 causes syntax error (cannot assign to constant).
   true errors (function requires arguments like true()).
   1 == 1 returns true.

2. Step 2: Identify the working method

   Only 1 == 1 correctly creates a logical true value.

3. Final Answer:

   1 == 1 -> Option A

4. Quick Check:

   1 == 1 = true [OK]

Hint: Use == in comparisons to get logical true [OK]

Common Mistakes:

• logical(0) returns false
• Using = instead of == for comparison
• Omitting () on true()

3. What is the output of this MATLAB code?

val = (4 < 2) | (7 == 7);
disp(val);

medium

A. Error

B. 0

C. 1

D. [0 1]

Solution

1. Step 1: Evaluate each logical expression

   4 < 2 is false (0), 7 == 7 is true (1).

2. Step 2: Apply the OR operator (|)

   False OR True results in true (1).

3. Final Answer:

   1 -> Option C

4. Quick Check:

   (false OR true) = true = 1 [OK]

Hint: OR is true if any side is true [OK]

Common Mistakes:

• Confusing OR (|) with AND (&)
• Expecting vector output
• Misreading comparison operators

4. Identify the error in this MATLAB code:

if 5 = 5
    disp('Equal');
end

medium

A. Using single = instead of == in if condition

B. Missing semicolon after disp statement

C. Incorrect use of disp function

D. No error, code runs fine

Solution

1. Step 1: Check the if condition syntax

   The single equal sign = is for assignment, not comparison.

2. Step 2: Correct the comparison operator

   Use double equal signs == to compare values in conditions.

3. Final Answer:

   Using single = instead of == in if condition -> Option A

4. Quick Check:

   Comparison needs ==, not = [OK]

Hint: Use == for comparison, = for assignment [OK]

Common Mistakes:

• Using = in if condition
• Ignoring MATLAB error messages
• Assuming semicolon is mandatory after disp

5. Given the vector A = [-1 0 1 2 0], which MATLAB expression returns a logical vector indicating which elements are nonzero?

hard

A. All of the above

B. A ~= 0

C. A > 0

D. A != 0

Solution

1. Step 1: Understand each expression

   A ~= 0 returns true where not zero.
   A != 0 uses invalid != operator (use ~=).
   A > 0 true only for positives.

2. Step 2: Check which elements each marks true for A = [-1 0 1 2 0]

   - A ~= 0: [true, false, true, true, false]
   - A != 0: syntax error
   - A > 0: [false, false, true, true, false]

3. Final Answer:

   A ~= 0 -> Option B

4. Quick Check:

   A ~= 0 = nonzero logical vector [OK]

Hint: Use ~= 0 to find nonzero elements [OK]

Common Mistakes:

• Using != instead of ~=
• Confusing ~= with ==
• Assuming >0 misses negative nonzero