1. 1 6001210-3 Discrete Mathematics Lecture1 Miss.Amal Alshardy

2. 2 Instruction Kenneth H. Rosen. Discrete Mathematics and Its Applications, 6th Edition Exams: 2 tests (40%), final (40%) Homework (10%): equally divided between several assignments.  HW submitted late will not be graded.  Cheating HW will not be graded Class attendance(10%) Each class slid should be with you. Textbook:

3. 3 Propositional Logic  Truth values, truth tables  Conjunction (  )  Negation (  )  Disjunction (  )  Implication (  )  Biconditional (  )  Exclusive OR(  )

4. 4 Propositions Declarative sentence(sentence that declares a fact) Must be either True or False. Propositions: UQU is in Makkah (T) 1+1=2 (T) 2+2=3 (F) jeddah is capital of Saudi Arabia (F) Not propositions: Do you like this class? Read this carrfully X+1=2 Are not declares a fact They are neither true nor false

5. 5 cont. Propositions Truth value: True or False proposition Variables: Variables that represent proposition.. We will use letters to denote proposition Variables: p,q,r,s,… Negation:  p (“not p”) Truth table for negation p pp TF FT

6. 6 cont. negating propositions  p: “is the opposite of the truth value of p”  p: “it is not the case that p” p: “it rained more than 20 inches in TO” p: “John has many iPads” Page 3 Find the negation of this two proposition

7. Conjunction: p  q [“and”] 7 pq p  qp  q TTT TFF FTF FFF e.g p: It is snowing q: It is below freezing N propositions 2 N possibility

8. 8 Page 3

9. 9 Disjunction: p  q [“or”] pq p  q TTT TFT FTT FFF e.g p: It is snowing q: It is below freezing

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11. 11 Exclusive OR (XOR) p  q – T if p and q have different truth values, F otherwise pq p  q TTF TFT FTT FFF

12. 12 Conditional:p  q [“if p then q”] p: hypothesis, q: conclusion E.g.:p: “If you turn in a homework late, then it will not be graded”; “If you get 100% in this course, then you will get an A+”.

13. Conditional:p  q [“if p then q”] 13 pqp  qp  q TTT TFF FTT FFT

14. 14 Conditional statement terminology

15. From the definition of a conditional statement find if this two statements are True or False and why??? “If today is Sunday,then 2+6=8” “If today is Sunday,then 2+6=3” 15

16. BiConditional:p q [“p iff q”] 16 pqp q TTT TFF FTF FFT Biconditional statement terminology

17. It is below freezing and it is snowing It is below freezing but not snowing It is not below freezing and it is not snowing It is either snowing or below freezing (or both) If it is below freezing, it is also snowing That it is below freezing is necessary and sufficient for it to be snowing 17 HW

18. Logical equivalent: 18

19. ((  P)↔Q)≡(P↔(  Q)) 19

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