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Artificial Intelligence - Propositional Logic
- 1. KNOWLEDGE REPRESENTATION Dr.T.M.SARAVANAN Associate Professor, Departmentof Computer Applications, Kongu Engineering College, Perundurai – 638 060.
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- 6. PROPOSITIONAL LOGIC Propositional Equivalences Two statements X and Y are logically equivalent if any of the following two conditions hold − The truth tables of each statement have the same truth values. The bi-conditional statement X⇔Y is a tautology.
- 7. PROPOSITIONAL LOGIC Propositional Equivalences Two statements X and Y are logically equivalent if any of the following two conditions hold − The truth tables of each statement have the same truth values. The bi-conditional statement X⇔Y is a tautology.
- 8. PROPOSITIONAL LOGIC Propositional Equivalences According to propositional logic is the following a tautology, a contradiction or a contingent? ¬(A∧(¬B))↔(A→B)
- 9. PROPOSITIONAL LOGIC Write thefollowing English sentences in symbolic form- 1. If it rains, then I will stay at home. The given sentence is- “If it rains, then I will stay at home.” This sentence is of the form- “If p then q”. So, the symbolic form is p → q where- p : It rains q : I will stay at home 2. If I will go to Australia, then I will earn more money. So, the symbolic form is p → q where- p : I will go to Australia q : I will earn more money
- 10. PROPOSITIONAL LOGIC Write thefollowing English sentences in symbolic form- 3. He is poor but honest. So, the symbolic form is p ∧ q where- p : He is poor q : He is honest 4. If a = b and b = c then a = c. So, the symbolic form is (p ∧ q) → r where- p : a = b q : b = c r : a = c 5. Neither it is hot nor cold today. So, the symbolic form is ∼p ∧ ∼q where- p : It is hot today q : It is cold today
- 11. PROPOSITIONAL LOGIC Write thefollowing English sentences in symbolic form- 6. He goes to play a match if and only if it does not rain. So, the symbolic form is p ↔ q where- p : He goes to play a match q : It does not rain 7. Birds fly if and only if sky is clear. So, the symbolic form is p ↔ q where- p : Birds fly q : Sky is clear 8. I will go only if he stays. So, the symbolic form is p → q where- p : I will go q : He stays
- 12. PROPOSITIONAL LOGIC Write thefollowing English sentences in symbolic form- 9. I will go if he stays. So, the symbolic form is p → q where- p : He stays q : I will go 10. It is false that he is poor but not honest. So, the symbolic form is ∼(p ∧ ∼q) where- p : He is poor q : He is honest 11.It is false that he is poor or clever but not honest. So, the symbolic form is ∼((p ∨ q) ∧ ∼r) where- p : He is poor q : He is clever r : He is honest
- 13. PROPOSITIONAL LOGIC Write thefollowing English sentences in symbolic form- 12. It is hot or else it is both cold and cloudy. So, the symbolic form is p ∨ (q ∧ r) where- p : It is hot q : It is cold r : It is cloudy 13. I will not go to class unless you come. So, the symbolic form is ∼ q → p where- p : I will go to class q : You come 14. We will leave whenever he comes. So, the symbolic form is p → q where- p : He comes q : We will leave
- 14. PROPOSITIONAL LOGIC Write thefollowing English sentences in symbolic form- 15. Either today is Sunday or Monday. So, the symbolic form is p ∨ q where- p : Today is Sunday q : Today is Monday 16. You will qualify GATE only if you work hard. So, the symbolic form is p → q where- p : You will qualify GATE q : You work hard 17. Presence of cycle in a single instance RAG is a necessary and sufficient condition for deadlock. So, the symbolic form is p ↔ q where- p : Presence of cycle in a single instance RAG q : Presence of deadlock
- 15. PROPOSITIONAL LOGIC Write thefollowing English sentences in symbolic form- 18. Presence of cycle in a multi instance RAG is a necessary but not sufficient condition for deadlock. So, the symbolic form is (q → p) ∧ ∼(p → q) where- p : Presence of cycle in a multi instance RAG q : Presence of deadlock 19. I will dance only if you sing. So, the symbolic form is p → q where- p : I will dance q : You sing 20. Neither the red nor the green is available in size 5. So, the symbolic form is ∼p ∧ ∼q where- p : Red is available in size 5 q : Green is available in size 5
- 16. PROPOSITIONAL LOGIC 1. Considerthe statement about a party, “If it's your birthday or there will be cake, then there will be cake.” a) Translate the above statement into symbols. Clearly state which statement is P and which is Q. b) Make a truth table for the statement. c) Assuming the statement is true, what (if anything) can you conclude if there will be cake? d) Assuming the statement is true, what (if anything) can you conclude if there will not be cake? e) Suppose you found out that the statement was a lie. What can you conclude?
- 17. PROPOSITIONAL LOGIC 1. Considerthe statement about a party, “If it's your birthday or there will be cake, then there will be cake.” a) P:P: it's your birthday; Q:Q: there will be cake. (P∨Q)→Q b) Hint: you should get three T's and one F. c) Only that there will be cake. d) It's NOT your birthday! e) It's your birthday, but the cake is a lie. 2. Make a truth table for the statement (P∨Q)→(P∧Q).
- 18. PROPOSITIONAL LOGIC 3. Makea truth table for the statement ¬P∧(Q→P). What can you conclude about P and Q if you know the statement is true? If the statement is true, then both P and Q are false. 4. Make a truth table for the statement ¬P→(Q∧R). 5. Determine whether the following two statements are logically equivalent: ¬(P→Q)¬(P→Q) and P∧¬Q.P∧¬Q. Explain how you know you are correct. 6. Are the statements P→(Q∨R) and (P→Q)∨(P→R) logically equivalent?