$.$ Consider the following formal language $($no semantics provided$)$:

$$ Alphabet: a$,$ b

$$ Syntax: the symbols a and baa are formulae. If $\backslash$psi and $$ are formulae then so are $\backslash$psi a$$

and aba$\backslash$psi $.$

Let A$(\backslash$psi $)$ be the number of a symbols in formula $\backslash$psi $,$ and let B$(\backslash$psi $)$ be the number of b symbols.

Use structural induction to prove that:

$.$A$()>=2$B$()$