Assume the Boolean matrix below is MR and that MR represents the relation R wher
ID: 1887721 • Letter: A
Question
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 ]
A) 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
B) Compute and interpret the Boolean products: MR ^2, and MR ^3. (Use Boolean arithmetic)
C) Now call the given matrix A and compute A^2 and A^3 using regular not Boolean arithmetic. What do these products give you.
Explanation / Answer
1)no flight b) WE KNOW A*A=A and A*A*A=A MR^2 = MR*MR = MR MR^3= MR*MR*MR = MR C)A^2 =A*A = a[ 1 2 1 0] b[ 0 1 2 1] c[ 1 1 1 1] d[1 2 1 1] A^3 = A^2*A = [ 1 3 3 1] [ 1 2 3 2] [ 2 3 2 1] [1 3 3 1]