T OR F

1.If X is a language over a non-empty alphabet and X^* is a finite language, X must be the empty language .

2.Let = {a, b} and let all variables be of the type "string over ". Let EA(w) mean "string w ends in a". Then the following is a valid proof of the statement "for all u: exists v: EA(uv)":

"Let u be an arbitrary string. Let v = 'a'. Then uv ends in a. By Existence, we have proved "exists v: EA(uv)". Since u was arbitrary, we have proved "for all u: exists v: EA(uv)"."