1. Section 1.1 Propositions and Logical Operations

2. Introduction Remember that discrete is –the study of decision making in non-continuous systems. That is, it is mathematics when there are a finite number of numbers.

3. Vocabulary Words logic proposition truth value compound proposition logical operation conjunction truth table disjunction exclusive or inclusive or negation

4. In-Class Activity #1 Get in groups of 3 or 4 students. Each person should print their name at the top of the paper I will hand out. As a group, complete Part One

5. Let’s test the CRS Go to Socrative Either in the app you downloaded or through a student login on the website. Enter Room ITTC328

6. Which of these is the best definition of “Logic” A = Statements that are either true or false B = The study of formal reasoning C = The study of whether or not things make sense D = a set of rules

7. Logic “Logic is the study of formal reasoning” (Mathematical logic is a tool for dealing with formal reasoning)

8. Logic In a nutshell: –Logic does: Assess if an argument is valid/invalid –Logic does not directly: Assess the truth of atomic statements

9. What is the Difference Logic can deduce that: –Cedar Falls is in the USA given these facts: –Cedar Falls is in Iowa –Iowa is a part of the USA and the definitions of: –‘to be a part of’ –‘to be in’ But logic knows nothing of whether these facts actually hold in real life!

10. Logic An Argument is a sequence of statements aimed at demonstrating the truth of an assertion The assertion at the end of the sequence is called the Conclusion, and the preceding statements are called Premises.

11. Logic A Statement (also Proposition) is a sentence that is true or false but not both Definition #2 on your sheet –A statement that is either true of false (but not both)

12. In-Class Activity #2 With your group, complete Part Two on your sheet.

13. One at a time let’s see what you think. 1.2 + 3 = 7 2.Julius Caesar was president of the United States. 3.What time is it? 4.Be quiet ! 5.The difference of two primes. 6.2 + 2 = 4 7.Washington D.C. is the capital of New York. 8.How are you?

14. Compound Propositions How did you define this in part one? –Connecting individual propositions with logical operations.

15. Compound Propositions Most of the things we do in logic look at combinations of several propositions. For example: –My number is both an even number and a prime number. –I am thinking of an odd number that is less than 20.

16. Logic In order to help us write “human language” based statements (I was going to type “English” but that’s probably not very accurate) in a more precise manner, we have come up with a variable-based and “mathematical” system for dealing with logic.

17. Logic To illustrate the logical form of arguments, we use letters of the alphabet (often p, q, and r) to represent the propositions of an argument.

18. Logic “My number is both an even number and a prime number.” p represents “my number is even” q represents “my number is prime” So we write: p and q

19. Logic Symbols There are a couple of base connectives that are common in logic. Each of these has been assigned a symbol. Not¬ And  Or  What are the “proper” names for these?

20. Truth Tables A truth table shows the relationship between various (often related) statements. It’s size depends on the number of independent variables represented in the statements –N independent atomic formulae (variables)  2 N rows

21. Negation p¬ p T F

22. Conjuction (and) pq p  q TT TF FT FF

23. Disjunction (or) pq p  q TT TF FT FF

24. In Class Activity #3 Complete Part Three with your team using the headers given below.

25. Activity Let –s = stocks are increasing –i = interest rates are steady How would we write –Stocks are increasing but interest rates are steady –Neither are stocks increasing nor are interest rates steady

26. Activity Let –M = Juan is a math major –C = Juan is a computer science major How would we write –Juan is a math major but not a computer science major