Given a set X and an operation op, X is closed under op, if for any x and y in X, (x op y) is also in X

a. N = {1,2,3,.} is closed under multiplication (Sipser p. 45). Explain (one sentence)

b. N is NOT closed under division. Explain

if X = {L : L is a finite language over {0,1},

c. List two languages in X

d. is X closed under union?

e. is X closed under concatenation?

if X = {L : L is a language over {0,1} and all strings in L have prime length},

f . List two languages in X

g. is X closed under intersection?

h. is X closed under concatenation?