#HomeWork#9
#Please do not post homework
#Abrar Almahmeed, Feb.22


#Question 1: 

NumberOfProperties:=proc(n,L,i)
local j,c:
c:=0:
for j from 1 to nops(L) do
if member(i,L[j]) then
   c:=c+1:
fi:
od:
c:
end:

NumberOfProperties(4,[{1,3},{2,4},{3,4}],1);
                               1

NumberOfProperties(4,[{1,3},{2,4},{3,4}],2);
                               1

NumberOfProperties(4,[{1,3},{2,4},{3,4}],3);
                               2

NumberOfProperties(4,[{1,3},{2,4},{3,4}],4);
                               2

#Question 2:

PIEgD:=proc(n,L,t):
local i,sum:
sum:=0:
for i from 1 to n do
sum:=sum+t^NumberOfProperties(n,L,i):
od:
sum:
end:

L:=[{1,3},{2,4},{3,4}]:
PIEgD(4,L,t);
                              2      
                           2 t  + 2 t

#Question 3:

for j from 1 to 5 do
L:=RandL(1000,4):
print(evalb(PIEg(1000,L,t)=PIEgD(1000,L,t))):
od:
                              true

                              true

                              true

                              true

                              true