The things in the set are called either members or elements. All the members of a set are members of a universal set (or for short: the Universe)

Transcription

1 9/4 Monday, September 1, :45 PM Quiz what was the last sentence I Tweeted to #shermat101 A set is a collection of things The things in the set are called either members or elements All the members of a set are members of a universal set (or for short: the Universe) The cardinality of a set is how many members it has The cardinality of A = A Report 1 due 9/23 HW U={a,b,c,d,e,f,g,h,I,j,k,lm,n,o,p,q,r,s,t,u,v,w,x,y,z} = {"the alphabet"} mat101nb Page 1

2 Report 1 due 9/23 HW Read 5.1 Pg U={a,b,c,d,e,f,g,h,I,j,k,lm,n,o,p,q,r,s,t,u,v,w,x,y,z} = {"the alphabet"} V={"the vowels"}={a,e,i,o,u} mat101nb Page 2

3 mat101nb Page 3 9/9 Tuesday, September 09, :48 PM Pg 267 {George Washington, John Adams} {4,5,7,6,9,8} {january,march,april,february,november,december,september,october} {dog,god,cod,cog} { New York,New Jersey, New Hampshire} {} = means exactly the same members A=B All the members of A are in B and all the members of B are in A Every element of A is in B 1. Set: Males Universe: Facebook stff Why: facebook has a smaller percentage of males than google HW: pg 268 Prob 32-41

4 mat101nb Page 4 9/11 Thursday, September 11, :31 PM quiz pg 268 prob 32,34,36,38,40 True or false 3pts Why its true or false 7pts From < F 7 is in A but not in B T every member of B is in A F 9 is in D but not a member of A F 6 is in A but not in C 1 is in B T F because the only member of D are 1 and 3 and 7 and 9 T Null set is a subset of everything F no Power set. Is the set of all subsets

5 mat101nb Page 5 U = {a,b,c,d,e} A={a,b} B={a,b,c} A) Contains all the subsets of A B) { HW Pg 268 prob Read 5.2 U = {a,b,c,d,e} A={a,b} B={a,b,c} C={b,c,d} Complement Everything in the universe that is not in A

6 mat101nb Page 6 Intersection To be a member of And also a member of C you must be a member of A PCIUD set theory PEMDAS

7 mat101nb Page 7 9/16 Tuesday, September 16, :41 PM Pg 268 prob 42, = 16=2*2*2*2 2*2*2*2*2*2-1=63 P C I U D () ' U={a,b,c,d,e,f,g} X={a,b,c,d} Y={b,d,f,g} Z={a,b,e,f} Y'={a,c,e}

8 mat101nb Page 8 Z'={c,d,g} X-Y Everything in X that is not in Y X-Y={a,c} Z={a,b,e,f}

9 mat101nb Page 9 PCIUD D'={1,5,6,7} HW pg 277 prob Read 5.3

10 mat101nb Page 10 9/18 Thursday, September 18, :34 PM quiz pg 277 prob 34 show work From < PCIUD 27. D'={1,4,5,6,7,10} D'-B = {1,4,5,6} 31. B' ={ 1,2,3,4,5,6,9} 32. C' ={1,2,4,6,8,9,10} D-C'={3} A'={2,5,6,8,9} B-A'={7,10}

11 mat101nb Page 11 Venn Diagrams U={a,b,c,d,e,f,g,h} X={a,b,c,d} Y={b,d,f,g} Z={a,b,e,f}

12 mat101nb Page 12 U={a,b,c,d,e} F={a,b} G={c,d} H = {a,b,e} Pg 285 ex 1. Ex 2. If two sets don't intersect they are disjoint D and E are disjoint D is a subset of C HW

13 Pg 287 prob read 5.3 mat101nb Page 13

14 mat101nb Page 14 9/23 Tuesday, September 23, :05 PM Unions and Intersections Report 2sets from the same universe Set1: Set2: Universe: Union (or Intersection) Why: Set1: Republican Congressman Set2: Democratic Congressman Universe: Comgressman Union Why: They all voted to bomb Syria Set1: Black Politicians Set2: Presidents of the US Intersection Universe: Politicians Why: Barak Obama requested authorization to bomb Syria Newspapers dated on or after 9/24/2014

15 mat101nb Page 15 41) 42) X=I,II Y=II,III X-Y=I

16 HW pg 288 prob mat101nb Page 16

17 mat101nb Page 17 9/30 Tuesday, September 30, :45 PM Newspaper report 2 Pg 13: Paris Milan Set1: Japan's trailblazers Set2: Western designers Universe: People (fashion people) Union Why: western designers are designing cool clothes based on japanese trailblazer Better Vision Set1: world's poor Set2: people who need corrective lenses Intersection Universe: people Why: efforts are under way to find a means of distributing inexpensive glasses Pg 17 Even for Cashiers Set1: European intelectuals Set2: students Union Universe: People Why: Intellectuals say not all students need high school. Set1: Cashiers Set2: College Students

18 mat101nb Page 18 Intersection Universe People Why: Cashiers who graduate make more money pg 288 prob 56, From < A = I,II A' = III,IV B= II,III B'=I,IV

19 mat101nb Page 19 Prob 63 A=I,II,III,IV B=I,II,V,VI Prob 67 A=I,II,III,IV B=I,II,V,VI C=I,III,V,VII 69 A=I,II,III,IV

20 mat101nb Page 20 C=I,III,V,VII B=I,II,V,VI HW pg 289 prob read 5.4

21 mat101nb Page 21 10/2 Thursday, October 02, :35 PM quiz pg 289 prob 68 From < A=I,II,III,IV A' = V,VI,VII,VIII B= I,II,V,VI B'=III,IV,VII,VIII A'-B'= V,VI (A'-B')'=I,II,III,IV,VII,VIII

22 mat101nb Page 22 C=V,I,III,VII 68. A=I,II,III,IV C=V,I,III,VI A-C=IV,II B'=III,IV,VII,VIII There were 100 people in a ballroom. 30 of them were dancing How many were not dancing. U = I( )+II( ) = 100 D = I( ) = 30 D' = II( )=70

23 mat101nb Page 23 25= U =I( 10 )+II( 3 )+III( 4 )+IV( 8 ) III(4) C =I(10)+II(3)=13 S = II(3)+III(4)=7 60= U =I(5 )+II( 8 )+III( 2 )+IV( 10 )+V( 7 )+VI( 13 )+VII( 5 )+VIII( 10 ) 30= R =I( 5 )+II( 8 )+IV( 10 )+V( 7 ) 30= P =II( 8 )+III( 2 )+V( 7 )+VI( 13 ) 35= G =IV( 10 )+V( 7 )+VI( 13 )+VII( 5 ) a. I(5) b. VIII(10) c. Irish but not German = R-G =I(5)+II(8)=13 HW pg prob 8-11

24 10/7 Tuesday, October 07, :41 PM quiz Of the 1000 in a school, 450 in mathematics, 300 in history and 75 in both. How many in neither? Show all work. From < 1000= U =I( 375 )+II( 75 )+III( 225 )+IV( 325 ) 450= M =I( 375 )+II( 75 ) 300= H =II( 75 )+III( 225 ) = = = 1,000 IV(325) How many are in history or math? How many are in history or not in math? mat101nb Page 24

25 19= G =I( 2 )+II( 3 )+IV( 2 )+V( 12 ) 19= S =II( 3 )+III( 0 )+V( 12 )+VI( 4 ) 20= B =IV( 2 )+V( 12 )+VI( 4 )+VII( 2 ) 15= 14= 16= a) III(0) b) II(3) c) d) G HW Read 5.5 mat101nb Page 25

26 Mat101 review exam 1 Tuesday, October 07, :12 PM A'={g,h,k,m,x,z} 2. F=I,II,IV,V H=IV,V,VI,VII H'=I,II,III,VIII a bcy f g h z k m x P G 30= U =I( )+II( )+III( )+IV( ) 10= P =I( )+II( ) 18= G =II( )+III( ) 22= so III=12 30= U =I( 4 )+II( 6 )+III( 12 )+IV( 8 ) 10= P =I( 4 )+II( 6 ) 18= G =II( 6 )+III( 12 ) 22= mat101nb Page 26

27 10/14 Tuesday, October 14, :48 PM E I II III IV V VI VII S M VIII 100= U =I( 25 )+II( 5 )+III( 34 )+IV( 8 )+V( 2 )+VI( 9 ) +VII( 6 )+VIII( 11 ) 50= M =II( 5 )+III( 34 )+V( 2 )+VI( 9 ) 25= S =IV( 8 )+V( 2 )+VI( 9 )+VII( 6 ) 40= E =I( 25 )+II( 5 )+IV( 8 )+V( 2 ) 11= 7= a) VII(6) b) VIII(11) mat101nb Page 27

28 Math or English? I(25)+II(5)+III(34)+IV(8)+V(2)+VI(9)=83 Don't need help with Social Studies= S' =I(25)+II(5)+III(34)+VIII(11)=75 Proportion S / U Proportion of students who don't need help with Social Studies? 75/100=0.75 =3/4 Proportion of students who need help in both english and SS? mat101nb Page 28

29 mat101nb Page 29 10/21 Tuesday, October 21, :45 PM M S I II III IV V VI VII C VIII 75= U =I( 5 )+II( 26 )+III( 0 )+IV( 28 )+V( 2 )+VI( 1 )+VII( 13 )+VIII( 0 ) 29= S =II( 26 )+III( 0 )+V( 2 )+VI( 1 ) 44= C =IV( 28 )+V( 2 )+VI( 1 )+VII( 13 ) 30= 28= 3= a) I(5) b) 75-29=46

30 60 at a party 40 males 30 smelled 25 of males smelled Proportion of males 40/60 = =2/3 P(M) Proportion of smelled 30/60 = 0.5 =1/2 P(S) Proportion of males that smelled 25/40 = P(S M) - conditional proportion Since Smelled and male are not independent/ mat101nb Page 30

31 mat101nb Page 31 10/23 Thursday, October 23, :44 PM Proportions report Pg 28 of handout Gender Google 1. Universe: Global google staff Set: males Proportion: 70% Why: to show that google could be much more diverse Pg 26 When teen 2. Universe: teen drivers listening to their preferred music. Proportion 98% Set: teens who demonstrated an average of 3 deficient driving behaviors Why: to show how music can distract teen drivers Pg 11 Cussin' Hollerin' We probably 3. Universe: customers Set: customers for Obama Proportion 1/1000 Why: to show how unpopular Obama was among deep south bikers Quiz 6 patients 4 fevers 3 rashes 1 neither. Rashes

32 mat101nb Page 32 proportion? Proportion of fever with rashes? Indpendent? From < &searchselect=_22167_1&context=course&course_id=_22167_1&internalhandle=cp_announcements&announcementid=_ 52573_1> Proportion rashes 3/6 = 0.5 F I II III IV R U I( )+II( )+III( )+IV( 1 ) =6 I( )+II( )=4 II( )+III( )=3 Proportion of fever with rashes P(R F) = Since P(R)=P(R F) then rashes are independent of fevers

33 mat101nb Page 33 U A I II III B IV A=I,II B=II,III B'=I,IV

34 mat101nb Page 34 10/28 Tuesday, October 28, :38 PM quiz pg 310 prob 16 show both sides of the equality are the same regions of the venn diagram From < A=I,II,III,IV B=I,II,V,VI A'=V,VI,VII,VIII B'=III,IV,VII,VIII

35 mat101nb Page 35 Pg 307 Rules 1 and 6-10 simplify Rules 2-5 and 11 rearrange Given L8 A=X Statement Reason X-X Given L11 A=X B=X L8 A=X Pg 309

36 mat101nb Page 36 L11 A=A B= L5 A=B' B =A L1 A=B L4 A=A B=B C=A' L8 A=A L10 A=A HW pg 310 prob 20-22

37 10/30 Thursday, October 30, :31 PM quiz pg 310 prob 20 as shown in class today From < L11 A is P B is R L5 A is P B is R' L1 A is R L3 A is P' B is R C is R' L8 A is R L10 A is P' L5 A is P B is S' L1 A is S L4 A is S' B is P' C is S L8 A is S L10 A is L11 A is S' Bis P 23. Statement A' Reason Given L8 A is B L10 A is A' We are done when no repeated letters mat101nb Page 37

38 no double complements U or 25. Statement Reason Given L4 A is A B is A' C is C L8 A is A L2 A is L10 A is HW pg 310 prob mat101nb Page 38

39 11/4 Tuesday, November 04, :43 PM a. b. c. d. e. f. g. h. i. L10 A is C L10 A is A' L11 A is C B is A' L1 A is A L5 A is C B is A L2 B is C A is L4 A is C B is C' C is A' L8 A is C L10 A is L11 A is C B is A 27. Statement Reason Given L5 A is B' B is A' L1 A is A L4 A is B' B is B'' C is A L8 A is B' L2 A is L10 A is mat101nb Page 39

40 mat101nb Page 40 11/6 Thursday, November 06, :35 PM Pg 311 prob 28 Statement Prob 29 Statement C' Reason Given L3 A is G B is G' C is H' L8 A is G L2 A is L10 A is H' Reason Given L5 A is C B is D L4 A is C' B is D C is D' L8 A is D L10 A is C' Prob 31 Statement Reason Given L11 A is P B is R L5 A is P B is R' L1 A is R

41 mat101nb Page 41 L4 A is P B is P' C is R L8 A is P L2 A is B is L10 A is Pg 317 a. Statement Reason Given L11 A is A B is B L11 A is A B is C' L4 A is A B is B' C is C'' L5 A is B' B is C'' L11 A is A B is

42 mat101nb Page 42 11/13 Mat101 review exam 2 Sunday, November 9, :20 PM

43 mat101nb Page 43 X=I,II Y=II,III Y-X=III X'=III,IV B II III S I IV V VI VII VIII R U Given L11 L11 L5 L1 L2 L6 A is M B is R A is A is M B is R' A is R A is M' B is A is M' B is R

44 mat101nb Page =I( 45 )+II( 18 )+III( 5 )+IV( 4 )+V( 3 )+VI(1 )+VII( 1 )+VIII( ) 70=I( 45 )+II( 18 )+IV(4 )+ V( 3 ) 27=II( 18 )+III(5 )+V( 3 )+VI( 1 ) 9=IV(4 )+V( 3 )+VI( 1 )+VII( 1 ) 6=III( 5 )+VI(1 ) 9=III( )+V( 3) +VI(1 ) P(B)= 70/90 = P(B S) = P(B R)= 21/27= a) independent 7/9= b) independent P(R)= 9/90 = 0.1 P(R S) = 4/27 = Statement Reason Given L11 A is Y B is X L2 A is Y B is X' L3 A is X' B is Y C is Y L7 A is Y L2 A is X' B is Y

45 mat101nb Page 45 11/20 Thursday, November 20, :57 PM p="delano Morgan will be president" q ="Logical statements require verbs" Logical connectives ~ Not (Negation) P N A O C B () ~ ~p "It is not true that Delano Morgan will be president" p ~p T F F T And (Conjunction) p ~p q T F T T F F F T T F T T T F F F F T F T F F F T Or (Disjunction) p ~p q

46 mat101nb Page 46 T F T T F F T T T T T F F T F F T F F F Implies (Implication) p ~p q T F T T T F T T T F T F F F T F T F T T Equivalent (Biconditional) p ~p q T F T T F T T F T F F F F T F T HW Pg 8 prob 22-40

47 11/24 Monday, November 24, :33 PM b Tf statement Tf statement c Conjunction Conditional Conditional, conjunction Conjunction e Conditional Negation Biconditional Negation Logic newspaper report (4) Conjuctions, Disjunctions, Conditionals Statement1: Statement2: Type: (conjuction,disjuction, conditional) Why: mat101nb Page 47

48 Conjunction words: and but also aswell Conditional words: if because? Disjunction words: or Disjunctions are about choice q ~q p T F T F F T T T T F F F F T F F HW Not a tautology mat101nb Page 48

49 1125 Tuesday, November 25, :45 PM Logic newspaper report Pg 28 2nd column "As for facebook's diversity " 1. Statement1: a report would come out soon Statement2: she didn't disclose what day it would be announced Type: Conjunction Why: to show the difficulty facebook has in addressing their diversity issues Pg "I remember" Statement1: I remember coming into the city Statement2: We were lost Type: conjunction Why: To explain why a situation was frightening 3. Pg 16 2nd column "Until recently " Statement1: institutions and academic centers have concentrated on making scans Statement2: They were collaborating with one another on themed projects. Type: Disjunction Why: to show how american institutions approach digital scanning % last column Statement1: our recommendations system is down Statement2: we degrade the quality of our responses Type: Conditional Why: to show how gmail responds to unreliability Quiz Pg 30 prob 12 PNAOCB P Q mat101nb Page 49

50 T T T T T F T F T T T F F T T F F F F T P ~p Q ~q T F T F F F T F T T F T T F T F F T T F T F T F T T F T Q R P T T T T T T T T F T T T T F T T T F T T T T T T F F F T F F F T T T T F F F T F F T T F F F T T F T F F F F F F F F F F F HW pg 38 prob mat101nb Page 50

51 mat101nb Page 51 12/2 Wednesday, November 26, :09 PM Quiz Which of a or b or c can be? (More than 1 or none of these may work in the truth table) Logical arguments If I don't eat I will be hungry If I am hungry then I snarl at people I did not snarl at people Therefore I ate An argument is valid if always when the premises are true the conclusion is true

52 mat101nb Page 52 g ~g c T F F T T F T F T F T F p q r ~r q v ~r T T T T F T F T T T F T T F F F F T T F F T T T F T T F T T F T T F F T F T T HW Read 2.1 Pg prob Counter example chart p q r T T T F T T

53 12/9 Tuesday, December 09, :37 PM Symbolize this argument: Either it is sunny or it is not raining. If its not a nice day, then it is cloudy and not sunny. It is not a nice day. Therefore it is raining or snowing. > It s a nice day = n It is sunny = s It is raining = r It is cloudy = c It is snowing = w n ~n s ~s c r ~r w T F F T T F T F F F T F T T T T T F F F T T F F F F F T F T F F F F T F T T T T F T T T T F T F T T T T F T T F F n s c r w F F T F F counterexample Pg 139 mat101nb Page 53

54 There is a south wind = s There will be rain = r There is an increase in barometric pressure =b s r ~r b ~b T T F F F T F T T T F T T F T T F T F mat101nb Page 54

55 12/11 Review Exam 3 Tuesday, December 09, :01 PM m ~m g z T F T F F T T T T T T T F F F F T F F F T T T F F F d ~d s ~( T F T T T F F F T T T F T T T F F F F T T F T F T F T T I bring my notes to the exam = n I remember everything = e I got a's = a exam Not on exam: a ~a e n T F F T T F mat101nb Page 55

56 T F F T T F F T F T T T F T F T F F mat101nb Page 56