Question

What is a compound Boolean expression?

Short answer

A compound Boolean expression is an expression that combines two or more simple Boolean expressions using logical operators such as AND, OR, and NOT. Simple Boolean expressions compare two values and result in either True or False. Logical operators are used to combine these simple expressions, with AND returning True if both expressions are True, OR returning True if either expression is True, and NOT returning the opposite of the expression it is applied to. Compound Boolean expressions are commonly used in programming for conditional statements, loops, and other control structures.

Step-by-step solution

Understanding Simple Boolean Expressions

A simple Boolean expression is an expression that compares two values using comparison operators such as equal to (==), not equal to (!=), less than (<), greater than (>), less than or equal to (<=), or greater than or equal to (>=). The result of a simple Boolean expression is either True or False. Examples of simple Boolean expressions are: x == y, a != b, and n <= 10.

Introducing Logical Operators

Logical operators are used to combine simple Boolean expressions. There are three main logical operators: 1. AND (represented by '&&' or 'and'): This returns True if both of the simple expressions are True, otherwise, it returns False. 2. OR (represented by '||' or 'or'): This returns True if any one of the simple expressions is True, otherwise, it returns False. 3. NOT (represented by '!' or 'not'): This returns the opposite of the expression it is applied to, i.e., if the expression has a truth value of True, it will return False, and vice versa.

Forming Compound Boolean Expressions

Now that we have a basic understanding of simple Boolean expressions and logical operators, we can create compound Boolean expressions using these elements. A compound Boolean expression is achieved by using one or more logical operators to combine two or more simple Boolean expressions. Here are some examples of compound Boolean expressions: 1. (x > 5) && (y < 10): This expression will return True if x is greater than 5 and y is less than 10. 2. (a == b) || (c != d): This expression will return True if either a is equal to b or c is not equal to d. 3. !(n >= 20): This expression will return True if n is not greater than or equal to 20, i.e., if n is less than 20. Compound Boolean expressions are typically used in programming for conditional statements, loops, and other control structures where multiple conditions must be checked.