S is a set of strings over the alphabet $\{a,b\}$ and is defined recursively as follows:

Basis: $inS$ and binS

Recursive rules: If $x$ is in $S,$ then bxainS and axbinS

Define the function $mB(x)$ to be the number of occurrences of the character $b$ in the string $x,$ and $mA(x)$ to be the number of occurrences of the character $a$ in the string $x.$ For example, $mB(bba)=2$ and $mA(bba)=1.$ Suppose that xinS. Select the fact that must be true about $x.$

$mB(x)=mA(x)+1$

$mB(x)mA(x)$

$0mB(x)-mA(x)1$

$0mA(x)-mB(x)1$