Tautologys_and_Fallacy_Presentation.pptx

Tautologys_and_Fallacy_Presentation.pptx

1. Cross math puzzle

2. 4 + 3 + 8 15 + x / 5 + 7 x 2 24 - - / 6 + 9 - 1 14 3 12 4

3. Cross math puzzles Cross Math puzzles are exercises in logic as well as math. To solve them, you must use logical reasoning to determine which numbers and operations fit into the puzzle grid. The skills required to solve Cross Math puzzles such as evaluating multiple conditions, narrowing down possibilities, and using deductive reasoning are the same skills you apply in logical arguments and problem-solving.

4. TAUTOLOGY AND FALLACY

5. TAUTOLOGY Tautology is a statement that is always true, regardless of the truth values of its components.

6. Modus Ponens (Tautology) Definition: If p → q (if p then q), and p is true, then q must also be true. Formula: p → q, p ⟹ q

7. Modus Ponens (Tautology) Examples: 1. If today is Saturday, then there is no school today. Today is Saturday therefore there is no school today. 2. If a person studies, then they will pass the exam. The person studies therefore t hey will pass the exam. 3. If a vehicle has fuel, then it will start. The vehicle has fuel therefore It will start.

8. Modus Tollens (Tautology) Definition: If p → q, and q is false, then p must also be false. Formula: p → q, ¬q ⟹ ¬p

9. Modus Tollens (Tautology) Examples: 1. If it is a dog, then it barks. It does not bark therefore i t is not a dog. 2. If today is Saturday, then there is school classes today. There is no school classes today therefore today is not Saturday. 3. If someone is a teacher, then they work in education. They do not work in education therefore t hey are not a teacher.

10. Disjunctive Syllogism (Tautology) Definition: If p ∨ q, and ¬p, then q must be true. Formula: p ∨ q, ¬p ⟹ q

11. Disjunctive Syllogism (Tautology) E xamples : 1. Either it’s a weekday or a weekend. It’s not a weekend therefore i t’s a weekday. 2. Either I will go swimming, or I will stay home. I did not go swimming therefore I stayed home. 3. Either the car is red or blue. It’s not red therefore i t’s blue.

12. Reasoning by Transitivity (Tautology) Definition: If p → q and q → r, then p → r. Formula: p → q, q → r ⟹ p → r

13. Reasoning by Transitivity (Tautology) Examples: 1. If it rains, then the ground will be wet. If the ground is wet, then plants will grow therefore If it rains, then plants will grow. 2. If John is a student, then he studies. If he studies, then he will pass therefore If John is a student, then he will pass. 3. If you exercise, then you gain strength. If you gain strength, then you can lift heavy objects therefore If you exercise, then you can lift heavy objects.

14. fallacy A fallacy is a mistaken belief, especially one based on unsound argument.

15. Fallacy of the Converse Definition: Mistakenly concluding that if p → q, then q → p.

16. Fallacy of the Converse Examples: 1. If it rains, then the ground is wet . Fallacy: If the ground is wet, then it must have rained. 2. If a shape is a square, then it has four sides . Fallacy: If a shape has four sides, then it is a square. 3. If someone is a doctor, then they went to medical school . Fallacy: If someone went to medical school, then they are a doctor.

17. Fallacy of the Inverse Definition: Mistakenly concluding that if p → q, then ¬p → ¬q.

18. Fallacy of the Inverse Examples: 1. If it is a cat, then it has fur . Fallacy: If it is not a cat, then it does not have fur. 2. If a vehicle is a car, then it has wheels . Fallacy: If a vehicle is not a car, then it does not have wheels. 3. If she is a mother, then she has a child . Fallacy: If she is not a mother, then she does not have a child.

19. assessment

20. Directions: Determine whether each of the following argument is a tautology or a fallacy. If it is sunny, then the park will be crowded. It is sunny therefore the park is crowded. If Sarah studies hard, she will pass the exam. Sarah studied Therefore; she passed the exam. If it is snowing, the temperature is below freezing. The temperature is not below freezing. Therefore; it is not snowing. If a person is in the choir, they like singing. This person does not like singing, therefore they are not in the choir.

21. Directions: Determine whether each of the following argument is a tautology or a fallacy. If Mary is a teacher, she teaches classes. If she teaches classes, she interacts with students. Therefore, if Mary is a teacher, she interacts with students. If a dog is trained, it will obey commands. If it obeys commands, it will behave well in public. Therefore, if the dog is trained, it will behave well in public. Either I will eat pasta or pizza for dinner. I did not eat pasta, so I ate pizza. Either the cat is outside, or it is in the house. The cat is not outside, so it must be in the house.

22. Directions: Determine whether each of the following argument is a tautology or a fallacy. If a person is a doctor, then they studied medicine. If a person studied medicine, so she must be a doctor. If a substance is toxic, it will cause harm if ingested. If this substance caused harm, so it must be toxic. If the plant gets sunlight, it will grow. If the plant did not get sunlight, so it will not grow. If a student studies, they will pass the exam. If this student did not study, so they will not pass the exam.