#OK to post homework
#Tianyi Liu,Sept 20, Assignment 4

1.
CP({a,b,c},{b,c,d});
{[a, b], [a, c], [a, d], [b, b], [b, c], [b, d], [c, b], [c, c], [c, d]}

CheckMult({1,2},{3,4});
true

CheckAdd({1,2,3},{3,4,5})
{1, 2, 3}, {3, 4, 5}, `have the following common elements `, {3}
FAIL

member([d,o,r,o,n],Words({d,o,n,r},5));
true

2.
A27 in OEIS has 77 numbers. Both 76 and 77 return the least number of hits which is 11. 
There is not an n such that returns only A27.

3.|U|=15. |A1|=5. |A2|=3. A1={3,6,9,12,15}. A2={5,10,15}. Comp(U,A1)={1,2,4,5,7,8,10,11,13,14}. 
Comp(U,A2)={1,2,3,4,6,7,8,9,11,12,13,14}. Comp(U,A1) intersect Comp(U,A2)={1,2,4,7,8,11,13,14}.
A1 intersect A2={15}
|Comp(U,A1) intersect Comp(U,A2)|=8=15-5-3+1

PIE2:=proc(U,A1,A2) local x,y:
if not type(A1,set) then
 print(A1, `is not a set `):
 RETURN(FAIL):
fi:

if not type(A2,set) then
 print(A2, `is not a set `):
 RETURN(FAIL):
fi:

if not type(U,set) then
 print(U, `is not a set `):
 RETURN(FAIL):
fi:

if A1 intersect U<>A1 then
 print(A1, `is not a subset of `, U):
 RETURN(FAIL):
fi:

if A2 intersect U<>A2 then
 print(A2, `is not a subset of `, U):
 RETURN(FAIL):
fi:

x:=Mynops((U minus A1) intersect (U minus A2)):
y:=Mynops(U)+Mynops(A1 intersect A2)-Mynops(A1)-Mynops(A2):

[x,y]:
end: