Find that negation for the following statement of a & b

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04-11-2022
Mathematics

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Find that negation for the following statement of a & b

Find That Negation For The Following Statement Of A Amp B class=

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SunshineJ213706idn SunshineJ213706idn · Answer 1 · 2022-11-04T05:27:48-04:00

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

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