Chapel Field Christian Schools
We will study basic logic in the form of sentence logic as well as memorize the truth tables you will use most frequently in programming. The exercises are taken with permission from the book A Modern Formal Logic Primer by Paul Teller. We will read and discuss the book together in class as well as independently.
Go to Quizlet and log in. If you’ve never created a Quizlet account, do so now using your school email. Then join the CSP 2018-19 class so you have access to the logic truth tables that you will need to memorize. You should plan to study these truth tables at least once per day.
Stop now and do one Learn session on the Truth Tables deck.
Have Mr. Olinda verify this checkpoint before moving on.
You will read Chapter 1 of A Modern Formal Logic Primer by Paul Teller for Checkpoints 2-7. Review pages 1-4 of Chapter 1 before completing the exercise.
Exercise 1-1: Explain in your own words what an argument is. Give an example of your own of an inductive argument and of a deductive argument. Explain why your example of an inductive argument is an inductive argument and why your example of a deductive argument is a deductive argument.
Your answer should be developed in writing and must be complete, simple, and concise. You will not move on to the next checkpoint unless your answer addresses each part of the exercise. Break the exercise down into smaller pieces and address each one. Write your answer as a reply to this post.
This exercise is due by February 19. Have Mr. Olinda verify this checkpoint before moving on.
Review pages 4-7 of Chapter 1 before completing the exercise.
Exercise 1-2: Transcribe the following sentences into sentence logic, using
Gto transcribePudding is good. andFto transcribePudding is fattening.
Have Mr. Olinda verify this checkpoint before moving on.
Review pages 7-9 of Chapter 1 and then write a one paragraph summary of Section 1-3 that is complete, simple, and concise. Write your answer as a reply to this post.
Have Mr. Olinda verify this checkpoint before moving on.
Review pages 9-10 of Chapter 1 before completing the exercise. As you prepare to complete Exercise 1-3, consider the following before you attempt to explain the concept in your own words.
The compound sentence “Smith believes that Tokyo has a larger population than New York” is not truth functional. There are two statements: Smith believes and Tokyo has a larger population than New York. Even if you know that Smith does believe Tokyo has a larger population or you know whether Tokyo does have a larger population, the way the sentence is connected makes it impossible to evaluate the conclusion as a combination of two true or false statements. In other words, you cannot break it into two smaller pieces that have a truth value. Is it true that Tokyo has a larger population than New York? We could prove or disprove that. However, how can we prove that Smith believes without the second half of the sentence?
The compound sentence “The penny comes up heads is more probable than the penny comes up tails” is not truth functional. In addition to being poorly worded for analysis because of the connective is more probable than, we also have two statements that cannot be evaluated independently and result in a definite conclusion. The penny could come up heads and not come up tails, but that does not give us insight into the probability of the events.
Exercise 1-3: Try to explain what it would be for a declarative compound sentence in English not to be truth functional. Give an example of a declarative compound sentence in English that is not truth functional. There are lots of them!
Your answer should be developed in writing and must be complete, simple, and concise. You will not move on to the next checkpoint unless your answer addresses each part of the exercise. Write your answer as a reply to this post.
Have Mr. Olinda verify this checkpoint before moving on.
Review pages 11-15 of Chapter 1 before completing the exercise.
Exercise 1-4: For each of the following sentences, state whether its main connective is ~, &, or v and list each sentence’s components. Then do the same for the components you have listed until you get down to atomic sentence letters. So you can see how you should present your answers, I have done the first problem for you.
Sentence Main Connective Components ~(Av~B) ~ Av~B Av~B v A, ~B ~B ~ B Work out the solutions to the following problems on paper and only type in the final solution. For example, the solution for the sample problem would be ~B.
Have Mr. Olinda verify this checkpoint before moving on.
Review pages 16-18 of Chapter 1 before completing the exercises.
Exercise 1-5: Which of the following expressions are sentences of sentence logic and which are not?
- A&~B
- A~&B
- Gv(B&H)
- A&(C&~(DvH))
- (A&B)v(C&D)
- (AvB)&CvD
Your answer should be developed in writing and must be complete, simple, and concise. You will not move on to the next checkpoint unless your answer addresses each part of the exercise. Write your answer as a reply to this post.
Exercise 1-6: Construct a complete truth table for each of the following sentences. The first one is done for you:
A B ~B ~BvA t t f t t f t t f t f f f f t t
- ~BvA
- ~(BvA)
- (QvT)&(QvT)
- (D&~G)v(G&D)
- Av(~BvC)
- Kv[P&(PvM)]
- [(Dv~B)&(DvB)]&(DvB)
- L&{Mv[N&(Mv~L)]}
Complete the truth tables on a separate piece of paper.
Have Mr. Olinda verify this checkpoint before moving on.
At this point you have been studying the truth tables for several days. In order to pass this checkpoint you must be able to accurately answer at least 70% of these when quizzed verbally. Then you will take the graded quiz.
Have Mr. Olinda verify this checkpoint before moving on.