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# Name:Treasa Bency Biju Jose
# Date: 09-18-2020
# Assignment #4

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I.

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

CheckDecomp({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, n, o, r}, 5));
                              true

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II.

n = 110 
Maple sequence: seq(i,i=1..110) gives exactly 1 hit on OEIS

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III.

PIE2 := proc(U, A1, A2) local n, m; 
if not type(U, set) then 
	RETURN(FAIL); end if; 
if not type(A1, set) then 
	RETURN(FAIL); end if; 
if not type(A2, set) then 
	RETURN(FAIL); end if; 
if A1 intersect A2 = {} then 
	RETURN(FAIL); end if; 
n := nops((U minus A1) intersect (U minus A2)); 
m := nops(U) - nops(A1) - nops(A2) + nops(A1 intersect A2); 
print([n, m]); 
end proc:

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IV.

PIE3 := proc(U, A1, A2, A3) local n, m; 
if not type(U, set) then 
	RETURN(FAIL); end if; 
if not type(A1, set) then 
	RETURN(FAIL); end if; 
if not type(A2, set) then 
	RETURN(FAIL); end if; 
if not type(A3, set) then 
	RETURN(FAIL); end if; 
if (A1 intersect A2) intersect A3 = {} then 
	RETURN(FAIL); end if; 
n := nops(((U minus A1) intersect (U minus A2)) intersect (U minus A3)); 
m := nops(U) - (nops(A1) + nops(A2) + nops(A3)) + (nops(A1 intersect A2) + nops(A1 intersect A3) 
	+ nops(A2 intersect A3)) - nops((A1 intersect A2) intersect A3); 
print([n, m]); 
end proc:

PIE3({1, 5, 10, 15, 20, 25, 30}, {10, 20, 30}, {15, 30}, {1, 10, 30});
                             [2, 2]


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V.

PIE4 := proc(U, A1, A2, A3, A4) local n, m; 
if not type(U, set) then 
	RETURN(FAIL); end if; 
if not type(A1, set) then 
	RETURN(FAIL); end if; 
if not type(A2, set) then 
	RETURN(FAIL); end if; 
if not type(A3, set) then 
	RETURN(FAIL); end if; 
if not type(A4, set) then 
	RETURN(FAIL); end if; 
if ((A1 intersect A2) intersect A3) intersect A4 = {} then 
	RETURN(FAIL); end if; 
n := nops((((U minus A1) intersect (U minus A2)) intersect (U minus A3)) intersect (U minus A4)); 
m := nops(U) - (nops(A1) + nops(A2) + nops(A3) + nops(A4)) + 
	(nops(A1 intersect A2) + nops(A1 intersect A3) + nops(A1 intersect A4) + nops(A2 intersect A3) 
	+ nops(A2 intersect A4) + nops(A3 intersect A4)) - (nops(A1 intersect A2 intersect A3) + 
	nops(A2 intersect A3 intersect A4) + nops(A1 intersect A3 intersect A4) + 
	nops(A1 intersect A2 intersect A4) + (nops(A1 intersect A2 intersect A3 intersect A4)); 
print([n, m]); 
end proc:

PIE4({5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75}, {5, 10, 15, 20, 25, 35, 45, 60},
	 {15, 25, 30, 35, 40, 45, 50, 65}, {10, 20, 25, 35, 40, 50, 55, 70},
	 {5, 10, 15, 25, 30, 40, 55, 75});
                             [0, 0]
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