The proofs for the following problems MUST be in the following form: Give the statement that you are going to prove Specify that the statement will be proven by induction on (name the induction parameter). Specify the base value of the induction parameter and prove the statement for the base . case State the induction hypothesis Perform the induction step using the assumption in the induction hypothesis Draw the conclusion by induction. 4) Given the alphabet {A,B), suppose that you have the following rules for constructing words in a language L2: a. Any single character from the alphabet is a word in language L2. b. Other than single character words, every word in L2 is one of the following: i. A word in L2 ending in character A, followed by the character B. ii. A word in L2 ending in character B, followed by the character A. Prove by weak mathematical induction that language L2 does not contain any word with two successive A's. The proofs for the following problems MUST be in the following form: Give the statement that you are going to prove Specify that the statement will be proven by induction on (name the induction parameter). Specify the base value of the induction parameter and prove the statement for the base . case State the induction hypothesis Perform the induction step using the assumption in the induction hypothesis Draw the conclusion by induction. 4) Given the alphabet {A,B), suppose that you have the following rules for constructing words in a language L2: a. Any single character from the alphabet is a word in language L2. b. Other than single character words, every word in L2 is one of the following: i. A word in L2 ending in character A, followed by the character B. ii. A word in L2 ending in character B, followed by the character A. Prove by weak mathematical induction that language L2 does not contain any word with two successive A's