Part $1$: Regular Expression Design

$1.$ Write regular expressions to express the following languages

Language A: All strings consisting of the letters $"$a$"$ and $"$b$"$ that do not contain two consecutive $"$aa$"$s$.$

Language B: The empty string or all strings starting with $"$a$"$ and ending with $"$b$".$

Language C: All strings containing at least two $"$a$"$s and two $"$b$"$s$.$

$2.$ NFA Design

$1.$ Design an NFA for each Language and show the state transition table. Explain your states and transitions.

$2.$ Visualize your NFA with a diagram.