Boolean Matrix: Airline Flights
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Assume the Boolean matrix below is MR, and that MR represents the relation R where R represents the connecting flights that an airline have between four cities: a,b,c,d. The 1 in row a column b means there is a flight from city a to city b. In general, there is a 1 in row x, column y if and only if there is a connecting flight between city x and city y. That is, the rows of the matrix represent the cities of the origins of the flights and the columns represent the destination cities.
a b c d
Let MR = a 1 1 0 0
b 0 1 1 0
c 0 0 1 1
d 1 1 0 0
(i) Let a stand for the airport in Manchester, let b stand for the airport in Boston, let c stand for the airport in Chicago, let d stand for the airport in Denver. Is there a flight from Denver to Chicago?
(ii) Compute and MR^2 and MR^3 (use Boolean arithmetic). What do these Boolean products give you? In other words, what do the Boolean entries in the matrices MR^2 and MR^3 mean?
(iii) Now call the given Matrix A and compute A^2 and A^3 using regular, not Boolean, arithmetic.
(iv) What does MR + MR^2 + MR^3 + MR^4 give me?
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This solution shows how to solve problems using Boolean arithmetic.
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(i) No, since the element of MR on row 1 and ...
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