# Please do not post homework
# Hari Amoor, 9/20/2020, Assignment 4

# Problem 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})

# false

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

# true

# Problem 2

# There is no such number, at least up to n=77.

# Problem 3

# The claim holds for A1, A2, U as defined. The cardinality of |Comp(U, A1) intersect Comp(U, A2)|
# is equal to |U| - |A1| - |A2| + |A1 intersect A2| = 15 - 5 - 3 + 7 = 14.

PIE2:=proc(U,A1,A2) local R:

R:=nops(U)-nops(A1)-nops(A2)+nops(A1 intersect A2):
[R,R]:

end: