Suppose A = {a1, . . . , am} and B = {b1, . . . , bn}. How many relations are there from A to B? Hint: Count the number of m × n matrices with (0,1)-entries. If R is a relation from A to B we define...

Suppose A = {a1, . . . , am} and B = {b1, . . . , bn}. How many relations are there
from A to B? Hint: Count the number of m × n matrices with (0,1)-entries.
If R is a relation from A to B we define the inverse relation R^-1 from B to A by bR^-1a whenever aRb.