The negation of the Boolean expression ~ s ∨ (~ r ∧ s) is...

Negation of given statement is

$= ~ \left[~ s ∨ \left(~ r ∧ s\right)\right]$

Using De Morgan's law $~ \left(A ∨ B\right) = ~ A ∧ ~ B$

$= ~ \left(~ s\right) ∧ ~ \left(~ r ∧ s\right)$

Using double negation law $~ \left(~ A\right) = A$, and De Morgan's law

$= s ∧ \left(~ \left(~ r\right) ∨ ~ s\right)$

$= s ∧ \left(r ∨ ~ s\right)$

Using distributive law $A ∧ \left(B ∨ C\right) = \left(A ∧ B\right) ∨ \left(A ∧ C\right)$

$= \left(s ∧ r\right) ∨ \left(s ∧ ~ s\right)$

$= \left(s ∧ r\right) ∨ F$

$= s ∧ r .$