Regarding sets $A$ and $B$
$$\begin{array}{ll}
p & : s(B \backslash A) = 1 \\
q & : s(A) \geq s(B) \\
r & : s(A \cup B) = 8
\end{array}$$
For the propositions
$$\left(p \Rightarrow r^{\prime}\right) \vee (q \wedge p)$$
it is known that the proposition is false.
What is the number of elements in $A \cap B$?
A) 8
B) 7
C) 6
D) 5
E) 4