Question

Find that negation for the following statement of a & b

Answer 1

Recall De Morgan's Law:

`\thicksim(p\land q)=(\thicksim p)\lor(\thicksim q)`

In this case,

`\begin{gathered} p=\text{ ''We are having pie''} \\ q=\text{ ''It is Jessica's birthday''} \end{gathered}`

Therefore,

`\begin{gathered} \sim p=\text{ ''We are not having pie''} \\ \sim q=\text{ ''It is not Jessica's birthday''} \end{gathered}`

Hence, the required negation follows from De Morgan's Law as:

`(\sim p)\lor(\sim q)=\text{ ''We are not having pie or it is not Jessica's birthday''}`

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