Negate the following sentences. If f is a polynomial and its degree is greater than 2, then $f^{\prime}$ is not constant.

Solution

Verified``If $f$ is a polynomial and its degree is greater than 2, then $\acute f$ is not constant.''

We want to negate this sentence. We can translate the sentence to: $P \wedge Q \implies (\sim R)$, where: $\color{#c34632}P$: $f$ is a polynomial. $\color{#c34632}Q$: The degree is greater than 2, $\color{#c34632}R$: $\acute f$ is not constant.

We know that $\sim(P \implies Q)=P \wedge (\sim Q)$

Thus, $\sim[(P \wedge Q) \implies (\sim R)] = (P \wedge Q) \wedge \sim (\sim R)= P \wedge Q \wedge R$

$\textbf{Negation:}$ $\text{\textcolor{#4257b2}{ $f$ is a polynomial and its degree is greater than 2 and $\acute f $ is constant. }}$

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