# Daniel Yang, Due Sept. 20, 9:00pm
# OK to post Homwork
# 1) Carefully study the Maple code for lecture 4 and find

#	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)

#	n = 106 (howevever, I got A262530 instead of A27)

# 3) 
	Help3 := proc() print(` PIE2(U,A1,A2)`); end proc;
	with(combinat);
	
	PIE2 := proc(U, A1, A2) local R, S, A, B; 
	if type(U, set) then
	else 
	 return FAIL; 
	fi;
	
	if type(A1, set) then
	else  
   	 return FAIL; 
	fi;
	
	if type(A2, set) then
	else 
	 return FAIL; 
	fi;
	
	if A1 subset U then 
	else
	 return FAIL; 
	fi; 

	if A2 subset U then
	else 
	 return FAIL; 
	fi:

	A := U minus A1; 
	B := U minus A2; 
	S := nops(A intersect B);

	R := nops(U) - nops(A1) - nops(A2) + nops(A1 intersect A2); 

	[S, R]; 
	end: