Consider the grammar G T- aT 1 and the language L = { w | w has at least three a's } Prove: 1. L(G) sL Here use induction over the number of steps in the derivation. 2. L s L(G) Here use induction over the length of a string. To receive full credit you must, for each of the above proofs State an induction hypothesis and call it P(n). You must call it this so I can grade easily. You must define P(n) precisely. It is different for each of the two directions of this proof, so consider each proof to be separate from the other Use weak or strong induction as necessary, but use P(k) P(k+1) to prove the induction step. If you need earlier values include those as well: P(k-1) etc. . Consider the grammar G T- aT 1 and the language L = { w | w has at least three a's } Prove: 1. L(G) sL Here use induction over the number of steps in the derivation. 2. L s L(G) Here use induction over the length of a string. To receive full credit you must, for each of the above proofs State an induction hypothesis and call it P(n). You must call it this so I can grade easily. You must define P(n) precisely. It is different for each of the two directions of this proof, so consider each proof to be separate from the other Use weak or strong induction as necessary, but use P(k) P(k+1) to prove the induction step. If you need earlier values include those as well: P(k-1) etc