Logical operators (&, |, ~) in MATLAB - Cheat Sheet & Quick Revision

Recall & Review

beginner

What does the & operator do in MATLAB?

The & operator performs element-wise logical AND between two arrays or logical values. It returns true only if both corresponding elements are true.

beginner

Explain the | operator in MATLAB.

The | operator performs element-wise logical OR between two arrays or logical values. It returns true if at least one of the corresponding elements is true.

beginner

What does the ~ operator do in MATLAB?

The ~ operator performs logical NOT. It inverts the logical value: true becomes false, and false becomes true.

intermediate

Given A = [true false true], B = [false true true], what is A & B?

A & B results in [false false true] because logical AND is true only where both A and B are true.

intermediate

How do logical operators help in filtering data in MATLAB?

Logical operators create logical arrays that can be used to select or filter elements from arrays based on conditions, making data processing easier.

What is the result of ~true in MATLAB?

A false

B true

C 1

D 0

The ~ operator inverts true to false.

Which operator performs element-wise logical OR in MATLAB?

A |

B &

C ~

D &&

The | operator performs element-wise logical OR.

If A = [1 0 1] and B = [0 1 1], what is A & B in MATLAB?

A [1 1 1]

B [0 0 0]

C [0 0 1]

D [1 0 0]

Logical AND returns true only where both elements are true (1).

What does the expression A | B return if A and B are logical arrays?

A Logical AND of A and B

B Logical XOR of A and B

C Logical NOT of A

D Logical OR of A and B

The | operator returns the logical OR of A and B.

Which operator would you use to invert a logical array in MATLAB?

A &

B ~

C |

D &&

The ~ operator inverts logical values.

Describe how the logical AND (&) and OR (|) operators work in MATLAB with examples.

Think about how two yes/no answers combine.

Explain the use of the logical NOT (~) operator and how it can be used to filter data in MATLAB.

Imagine flipping a switch from on to off.

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