Propositional logic
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The document discusses the concept of logical propositions and how to determine their truth values through examples. It emphasizes that a logical proposition must assert something that can be evaluated as true or false, and it explores various examples of statements to identify which are propositions. The document also includes exercises on forming negations of propositions and group discussions to analyze logical expressions.
Propositional logic
- 1. Do U argue logically?
- 2. How? You say or propose a logical statement Your proposition is logical if the truth of the statement can be determined. Your proposition is a statement if it states a logic.
- 3. Is it a statement? Can it be determined whether it is true or false?
- 4. Carlos is a boy Is Carlos a boy? y$ + x$ = “boy” Pair up. Discuss the 3 expressions. Which one/s are logical propositions?
- 5. Carlos is a boy Is Carlos a boy? y$ + x$ = “boy” Truth can be checked. Do not know y$ or x$, therefore cannot determine truth of the expression. This is a question. Not a statement. Proposes - states
- 6. So to be a proposition It should state something We should be able to determine the truth of the statement Sometimes it is easier to determine the truth of a negative statement: Carlos is not a tree
- 7. The propositional statement can change, therefore can it be called a variable? For example:- Carlos is a girl or Carlos is a man or Carlos is a woman, etc. Area of logic includes girl, man, woman, boy, human, etc. Carlos is a boy p
- 8. p = Carlos is a boy Can the variable be T for True or F for False? How? If Carlos is actually a man then Is p = T or p = F? If we want to state: Carlos is NOT a boy? How can we write this? ¬
- 9. p = Carlos is a boy If Carlos is actually a boy, is ¬ p true? Pair up. Decide on all possible combinations of the variable p. Now put all combinations in a table. What can we call this table?
- 10. Class to break up into four groups. Each group to take ONE problem and show the solution on a poster.
- 11. Which of these sentences are propositions? What are the truth values of those that are propositions? a) Boston is the capital of Massachusetts. b) Miami is the capital of Florida. c) 2 + 3 = 5. d) 5 + 7 = 10. e) x + 2 = 11. f ) Answer this question
- 12. Which of these are propositions? What are the truth values of those that are propositions? a) Do not pass go. b) What time is it? c) There are no black flies in Maine d) 4 + x = 5. e) The moon is made of green cheese. f ) 2n ≥ 100.
- 13. What is the negation of each of these propositions? a) Mei has an MP3 player. b) There is no pollution in New Jersey. c) 2 + 1 = 3. d) The summer in Maine is hot and sunny.
- 14. What is the negation of each of these propositions? a) Jennifer and Teja are friends. b) There are 13 items in a baker’s dozen. c) Abby sent more than 100 text messages every day. d) 121 is a perfect square.