Recall De Morgan's Law:
[tex]\thicksim(p\land q)=(\thicksim p)\lor(\thicksim q)[/tex]In this case,
[tex]\begin{gathered} p=\text{ ''We are having pie''} \\ q=\text{ ''It is Jessica's birthday''} \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} \sim p=\text{ ''We are not having pie''} \\ \sim q=\text{ ''It is not Jessica's birthday''} \end{gathered}[/tex]Hence, the required negation follows from De Morgan's Law as:
[tex](\sim p)\lor(\sim q)=\text{ ''We are not having pie or it is not Jessica's birthday''}[/tex]The required negation is:
(A) "We are not having pie or it is not Jessica's birthday"
(B) The given statement is:
It is not the case that "walnuts grow on lily pads or caterpillars turn into butterflies"
By using De Morgan's Law, the equivalent statement is as follows:
Walnuts don't grow on lily pads and caterpillars don't turn into butterflies