Problem 2 . Use induction on n, to prove that for any alphabet T and any natural number n, the strings of length n have cardinality Tn. For instance, if the alphabet has three letters, then there exists 37 strings of length 7 . Proceed to the proof by proving that F:Tn+1Tn+1({n}T) where F()=(,(n,r(0)) eg. F(abc)=(ab,(2,c)), for n=3. We will use also a fact from discrete mathematics that AB=AB