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Before diving into the workings of a dual alternative decision structure, it is important to understand the following terms: - Condition: It is a statement that evaluates to a boolean value, either true or false. - Decision structure: A control structure that allows a program to perform different actions based on whether a specific condition is true or false. - Dual alternative decision structure: A type of decision structure that has two alternative paths for execution. One path is taken if the condition is true, and the other path is taken if the condition is false.

Here's a step-by-step explanation of how a dual alternative decision structure works: 1. The program encounters a condition to be evaluated. 2. If the condition is true, the program executes the block of code associated with the true case and then continues its execution after the dual alternative decision structure. 3. If the condition is false, the program executes the block of code associated with the false case and then continues its execution after the dual alternative decision structure. 4. The program proceeds to the next line of code after the dual alternative decision structure.

Most programming languages provide specific syntax for implementing a dual alternative decision structure. Commonly used syntax includes "if-else" statements in languages like C, C++, Java, Python, and many others. Here's a basic example in Python: ``` if condition: # Code to be executed if the condition is true else: # Code to be executed if the condition is false ```

Let us demonstrate a dual alternative decision structure in action with a simple example. We will take a numerical grade and determine if the student has passed or failed. input: grade = 75 Algorithm: 1. Check if the grade is greater than or equal to 50. 2. If the grade is greater than or equal to 50, print "Passed." 3. If the grade is less than 50, print "Failed." Python code: ``` grade = 75 if grade >= 50: print("Passed") else: print("Failed") ``` Output: "Passed" In this example, the condition "grade >= 50" is evaluated. Since the grade is 75, the condition is true, so the program executes the code under the "if" block and prints "Passed". If the grade were less than 50, the program would print "Failed" because the condition would be false.