In: Advanced Math
14.6. Say that a string x overlaps a string y if there exist strings p, q, r such that x = pq and y = qr, with q ̸= λ. For example, abcde overlaps cdefg, but does not overlap bcd or cdab.
(a) Draw the overlap relation for the four strings of length 2 over the alphabet {a, b}.
(b) Is overlap reflexive? Why or why not?
(c) Is overlap symmetric? Why or why not?
(d) Is overlap transitive? Why or why not?