5) For each of the following claims, state whether it is True or False. Prove your answer.
a) If L = L1 L2 and L is regular then L1 and L2 must be regular.
b) (¬(¬L) is regular) → (L is regular).
c) (L1 - L2 is regular) → (L1 is regular).
d) (L^R is regular) → (L is regular).
e) For any language L, L ∪ {a^nb^n : n ≥ 0} must not regular.
f) Given any language L, it cannot be true that L - {a^nb^n : n ≥ 0} is regular.
g) The finite languages are closed under Kleene star