Seminar 4 Event Algebra.R.txt

Dice <- 1:6
sample(Dice, 1)

set1<-sample(Dice, replace=F, 3) #throw a dice 3 times
set2<-sample(Dice, replace=F, size=4) #throw a dice 4 times
set3<-sample(Dice, replace=T, 4) #бросить кость 4 раза с повтором

# how to simulate random events
Coin <- c("Head", "Tail")    # Create a vector named Coin
print(Coin) #The sample space

sample(x = Coin, size = 1, replace = TRUE, prob = c(1/3,2/3)) # Throw a coin for size=1 time
sample(x = Coin, size = 3, replace = TRUE, prob = c(1/3,2/3)) # Throw a coin for size=3 times

#Intersections of events
intersect(set1, set2) # intersecting 2 sets
intersect(set2, set3)
intersect(set1,intersect(set2,set3)) # intersecting 3 sets


union(set2, set1) #union 2 sets
union(union(set1, set2),set3) #union 3 sets


setdiff(set3, set1) # all elements in set1 if they are not in set2

setequal(set1, set2) #is set1 equal to set2

#explain
setequal(union(set1, set2),
         c(setdiff(set1, set2), intersect(set1, set2), setdiff(set2, set1)))

unique(set3<-sample(Dice, replace=T, 5)) #transform to a vector with non repeated values

A<-c(0,1)
notA<-c(1,0) 
#or
!A #negate a binary set
B<-c(0,1)
notB=notA
union(A,notB) #left part
union(A,intersect(notA,notB)) #right part
#or
setequal(union(A,notB),union(A,intersect(notA,notB)))

#learn more here
#https://rstudio-pubs-static.s3.amazonaws.com/318220_fe0f62e9f9bf4ab9a00858631872b65e.html

set4<-c(1,0,0,1)
!set4 #negate a binary set

# Load library
library(VennDiagram)
# Chart

draw.single.venn(area = 10)     # Create single venn diagram
venn.plot<-venn.diagram(x = list(set1, set2, set3), category.names = c("Set 1" , "Set 2 " , "Set 3"),filename = NULL)
grid.draw(venn.plot);
grid.newpage()                                        # Move to new plotting page



grid.newpage()                                        # Move to new plotting page
draw.pairwise.venn(area1 = set1,                        # Create pairwise venn diagram
                   area2 = set3,
                   cross.area = 1)