Regarding a two-digit natural number $AB$, the following propositions are given:\\
p: The number $AB$ is even.\\
q: The number $A^{AB}$ is prime.\\
r: $A + B = 11$
If the proposition $(p \Rightarrow q) \wedge (q' \wedge r)$ is true, what is the product $A \cdot B$?\\
A) 18\\
B) 20\\
C) 24\\
D) 28\\
E) 30