Show that the class P is closed under concatenation, i.e.. if L_1. L_2 are any two languages in P then their concatenation L_1L_2 is also in P. Show that NP is closed under the Kleene star operation, i.e.. if L is any language in NP then L* is also in NP. (Both P and NP are closed under concatenation, star, union, intersection, but you do not have to show these. P is also closed under complement, but NP is not believed to be closed under complement.)
