Untitled Flashcards Set

## **True or False: Discrete Structures and Problem Solving (Answers)**

1. **False** – Discrete Mathematics deals with distinct values, not continuous number lines.

2. **True** – Discrete structures involve discrete elements with defined operations.

3. **True** – Graph Theory and Boolean Algebra are core topics in Discrete Mathematics.

4. **True** – The "GUESS" method consists of Givens, Unknown, Equation, Solution, and Survey.

5. **False** – Polya’s framework has four steps: Understanding the Problem, Devising a Plan, Carrying Out the Plan, and Looking Back.

6. **False** – In continuous mathematics, between any two numbers, there is an infinite number of values.

7. **False** – Problem-solving does not follow a universal method; it involves different approaches and strategies.

8. **True** – A uniform cost method can be used to analyze solutions.

9. **True** – The "Looking Back" step verifies the correctness of the solution.

10. **False** – Discrete Mathematics is widely used in computer science, including algorithms, cryptography, and database management.

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## **Identification: Key Terms and Answers**

1. **Discrete Mathematics** – A branch of mathematics involving discrete elements that uses algebra and arithmetic.

2. **Continuous Mathematics** – The category of mathematics dealing with a continuous number line, often involving calculus.

3. **Survey** – The step in problem-solving where you analyze whether the solution is realistic.

4. **Graph Theory** – A concept in discrete structures that involves nodes connected by edges.

5. **Trees** – A type of discrete structure that represents hierarchical relationships (e.g., parent-child connections).

6. **Polya’s Framework** – The problem-solving framework that involves understanding the problem, devising a plan, executing, and looking back.

7. **Equation** – The step in problem-solving where you select a mathematical equation to solve a given problem.

8. **Proof by Contradiction** – The type of proof method that assumes the opposite of the desired conclusion and shows it leads to a contradiction.

9. **Solution Analysis** – A structured method to determine the best solution among different possibilities.

10. **Problem Formulation** – The four items that define a problem (initial state, operators, goal test, path cost).