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Chapter 3: Problem 14

What is a compound Boolean expression?

Short Answer

Expert verified
Answer: A compound Boolean expression is a logical expression that combines two or more simple Boolean expressions using logical operators such as AND (&& or &), OR (|| or |), and NOT (! or ~). These expressions return a result of either true or false depending on the input values and the logical operators used. To create a compound Boolean expression, you can combine simple Boolean expressions using these logical operators. For example, a compound expression could look like (A && B) || C, where A, B, and C are simple Boolean expressions. This expression evaluates to true if both A and B are true or if C is true.

Step by step solution

01

Definition of a compound Boolean expression

A compound Boolean expression is a logical expression that combines two or more simple Boolean expressions using logical operators like AND (&& or &), OR (|| or |), and NOT (! or ~). These expressions return a result of either true or false depending on the values of the input and the chosen logical operators.
02

Common logical operators in compound Boolean expressions

There are three main logical operators used in compound Boolean expressions: 1. AND (&& or &): This operator returns true if both input values are true. Otherwise, it returns false. 2. OR (|| or |): This operator returns true if at least one of the input values is true. If both inputs are false, it returns false. 3. NOT (! or ~): This operator returns the opposite value of the input. If the input is true, it returns false. If the input is false, it returns true.
03

Example of a compound Boolean expression

Let's create an example of a compound Boolean expression using the logical operators mentioned above: Suppose we have three simple Boolean expressions A, B, and C: - A: x > 5 - B: y < 10 - C: z != 3 We can combine these expressions using the AND and OR operators. For example, we want to check if x > 5 AND y < 10 OR z != 3. The compound Boolean expression would look like this: (A && B) || C This expression will evaluate to true if x > 5 and y < 10, or if z is not equal to 3.

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