Question

What is a compound Boolean expression?

Short answer

#tag_title#Short Answer A compound Boolean expression is a combination of simpler Boolean expressions using logical operators (AND, OR, and NOT) to evaluate complex conditions. The three primary logical operators are AND (if both expressions are true), OR (if at least one expression is true), and NOT (negates the truth value of the expression). These expressions are used in programming and decision making.

Step-by-step solution

Introduction to Compound Boolean Expressions

A compound Boolean expression is basically a combination of simpler Boolean expressions using logical operators, such as AND, OR, and NOT. These expressions help in evaluating complex conditions in programming and decision making. The result of a compound Boolean expression is always either true or false.

Logical Operators

There are three primary logical operators that are used in compound Boolean expressions: 1. AND (also represented as &&): If both expressions are true, then the compound expression is true. 2. OR (also represented as ||): If at least one expression is true, then the compound expression is true. 3. NOT (also represented as !): If the expression is true, then its negation (NOT expression) is false; and if the expression is false, its negation is true.

Example 1: Using AND Operator

Consider the following expressions: A: The weather is sunny. B: The temperature is above 20°C. A compound Boolean expression using the AND operator can be written as: (A AND B): The weather is sunny, and the temperature is above 20°C. The compound expression (A AND B) is true only if both the expressions A and B are true.

Example 2: Using OR Operator

Continuing with expressions A and B, a compound Boolean expression using the OR operator can be written as: (A OR B): The weather is sunny, or the temperature is above 20°C. The compound expression (A OR B) is true if at least one of the expressions A or B is true.

Example 3: Using NOT Operator

Consider the expression C: C: It is not raining. The negation (NOT C) of this expression is: NOT C: It is raining. If the expression C is true (it is not raining), then NOT C is false (it is raining).

Combining Logical Operators

You can also combine multiple logical operators in a single compound Boolean expression. For example, consider the following expressions: Expression D: The temperature is below 0°C. Expression E: It is snowing. A compound Boolean expression can be written as: ((A AND B) OR (D AND E)): (The weather is sunny, and the temperature is above 20°C) OR (The temperature is below 0°C, and it is snowing). This compound expression is true if either (A AND B) or (D AND E) are true.