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Chapter 4: Problem 4

What is a Boolean expression?

Short Answer

Expert verified
Answer: A Boolean expression is a logical statement that results in a true or false outcome, consisting of variables, operators, and literals. Some examples of Boolean expressions are x ∧ y (true if both x and y are true), a ∨ b (true if either a or b is true), ¬x (true if x is false), and (x ∧ y) ∨ (¬z) (true if both x and y are true or if z is false).

Step by step solution

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1. Definition of a Boolean Expression

A Boolean expression is a logical statement that results in a true or false outcome. It is named after the mathematician George Boole, who developed the concept of Boolean algebra. Boolean expressions are used in various fields, such as computer programming, digital electronics, and logic design.
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2. Components of a Boolean Expression

A Boolean expression consists of variables, operators, and literals. Variables represent the unknown values in the expression, while literals represent the true or false values. Operators are the mathematical symbols used to combine or manipulate the variables, such as AND, OR, and NOT.
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3. Boolean Operators

There are three primary Boolean operators used in Boolean expressions: 1. AND - represented by the symbol \(\wedge\). It returns true only when both operands are true. 2. OR - represented by the symbol \(\vee\). It returns true when at least one of the operands is true. 3. NOT - represented by the symbol \(\neg\). It returns true when the operand is false, and vice versa.
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4. Examples of Boolean Expressions

Here are some examples of Boolean expressions: 1. x \(\wedge\) y - this expression returns true only if both x and y are true. 2. a \(\vee\) b - this expression returns true if either a or b is true (or both are true). 3. \(\neg\) x - this expression returns true if x is false, and vice versa. 4. (x \(\wedge\) y) \(\vee\) (\(\neg\) z) - this expression returns true if both x and y are true or if z is false. These examples demonstrate some simple Boolean expressions that evaluate to true or false based on the values of the variables and literals and the relationships created by the operators.

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Most popular questions from this chapter

If the following pseudocode were an actual program, what would it display? Declare String s1 = "New York" Declare String s2 = "Boston" If s1 > s2 Then Display s2 Display s1 Else Display s1 Display s2 End If

Write an If-Then statement that displays the message "The number is not valid" if the variable speed is outside the range 0 through 200 .

When you write an If-Then-Else statement, under what circumstances do the statements that appear between the Else clause and the End If clause execute?

What is a decision structure?

What statement do you use in pseudocode to write a dual alternative decision structure?
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