Given the alphabet {A,B}, suppose that you have the following rules for constructing words in a language L2:

1.Any single character from the alphabet is a word in language L2.

2.Other than single character words, every word in L2 is one of the following:

1.A word in L2 ending in character A, followed by the character B.

2.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 As.