1. Given the alphabet {0, 1}, {0, 1}* is defined to be all the strings that can be obtained by concatenating zero or more symbols from {0, 1}. Let L1 and L2 be subsets of {0, 1}*, and consider the two languages L* UL2* and (L1 L2)*. a) Which of the two is always a subset of the other? Why? Give an example (i.e., say what L1 and L2 are) such that the opposite inclusion does not hold. b) Give an example of languages L1 and L2 such that L1* L2*, L2* L*, L* L2*, and L* UL2* = (L1 UL2)*.