Question: Assume the Boolean matrix below is M_R and that M_R 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.

(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: M_R² , and M_R³ . (Remember to use Boolean arithmetic). What do these Boolean products give you?

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