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}) = false
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.
There is no list 1..n that will return only the one hit A27. The longest list you can search for is where n = 77 (1..77), which return A27 along with 10 other entries. The OEIS search only correlates A27 with 1 through 77, so any n over 77 will not return A27. 

3. 
U={1,...,15}
A1={3,6,9,12,15}
A2={5,10,15} 
|U|-|A1|-|A2|+|A1 intersect A2| = 15 - 5 - 3 + 1 = 8

PIE2:=proc(U,A1,A2):
[nops(U)-nops(A1)-nops(A2)+nops(A1 intersect A2),nops(U minus A1 intersect U minus A2)]:
end: