Consider the following set of facts for the relation PARENT(X, Y), where Y is the parent of X:

PARENT(a, aa), PARENT(a, ab), PARENT(aa, aaa), PARENT(aa, aab),

PARENT(aaa, aaaa), PARENT(aaa, aaab)

Consider the rules
r₁: ANCESTOR(X, Y) :– PARENT(X, Y)
r₂: ANCESTOR(X, Y) :– PARENT(X, Z), ANCESTOR(Z, Y)

which define ancestor Y of X as above.

a. Show how to solve the Datalog query

ANCESTOR(aa, X)?

and show your work at each step.

b. Show the same query by computing only the changes in the ancestor relation and using that in rule 2 each time.