Assume the Boolean matrix below is MR and that MR represents the relation R where R represents the connecting flights that an airline has between 4 cities: a, b, c, and d. so there is a 1 in row x column y iff there is a connecting flight between (from) city x and (to)city y That is, the rows of the matrix represent the cities of the origins of the flight and the columns represent the destination cities.

a b c d
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 the city of Manchester, let b stand for the airport in Boston, c stand for the Chicago airport, d for the airport in the city of Denver. Is their a flight from Manchester to Chicago?

(ii) Compute and interpret the Boolean products: MR 2, and MR 3. (Remember to use Boolean arithmetic)

(iii) Now call the given matrix A and compute A2 and A3 using regular not Boolean arithmetic. What do these products give you.

(iv) Again call the given matrix A and assume there are 3 flights Boston to Chicago and four from Chicago to Denver and compute A2.

What does MR + MR 2 + MR 3 + MR 4 give you?