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Write out the truth table for $ \lnot \bigl(\left( \lnot P \Rightarrow Q\right) \Rightarrow R\bigr)$.
Hint: $\land$ is AND. $\lor$ is OR. $\lnot$ is NOT. $\Rightarrow$ is IMPLIES. $\Leftrightarrow$ is IFF. $\oplus$ is XOR.
$C_1$$C_2$$C_3$
$P$$Q$$R$$ \lnot P$$C_1 \Rightarrow Q$$C_2 \Rightarrow R$$ \lnot C_3$
$\mathsf{T}$$\mathsf{T}$$\mathsf{T}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r0c0}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r0c1}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r0c2}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r0c3}}\hspace{35px}}~}$
$\mathsf{T}$$\mathsf{T}$$\mathsf{F}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r1c0}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r1c1}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r1c2}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r1c3}}\hspace{35px}}~}$
$\mathsf{T}$$\mathsf{F}$$\mathsf{T}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r2c0}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r2c1}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r2c2}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r2c3}}\hspace{35px}}~}$
$\mathsf{T}$$\mathsf{F}$$\mathsf{F}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r3c0}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r3c1}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r3c2}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r3c3}}\hspace{35px}}~}$
$\mathsf{F}$$\mathsf{T}$$\mathsf{T}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r4c0}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r4c1}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r4c2}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r4c3}}\hspace{35px}}~}$
$\mathsf{F}$$\mathsf{T}$$\mathsf{F}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r5c0}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r5c1}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r5c2}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r5c3}}\hspace{35px}}~}$
$\mathsf{F}$$\mathsf{F}$$\mathsf{T}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r6c0}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r6c1}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r6c2}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r6c3}}\hspace{35px}}~}$
$\mathsf{F}$$\mathsf{F}$$\mathsf{F}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r7c0}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r7c1}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r7c2}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r7c3}}\hspace{35px}}~}$
$C_1$$C_2$$C_3$
$P$$Q$$R$$ \lnot P$$C_1 \Rightarrow Q$$C_2 \Rightarrow R$$ \lnot C_3$
$\mathsf{T}$$\mathsf{T}$$\mathsf{T}$$\mathsf{F}$$\mathsf{T}$$\mathsf{T}$$\mathsf{F}$
$\mathsf{T}$$\mathsf{T}$$\mathsf{F}$$\mathsf{F}$$\mathsf{T}$$\mathsf{F}$$\mathsf{T}$
$\mathsf{T}$$\mathsf{F}$$\mathsf{T}$$\mathsf{F}$$\mathsf{T}$$\mathsf{T}$$\mathsf{F}$
$\mathsf{T}$$\mathsf{F}$$\mathsf{F}$$\mathsf{F}$$\mathsf{T}$$\mathsf{F}$$\mathsf{T}$
$\mathsf{F}$$\mathsf{T}$$\mathsf{T}$$\mathsf{T}$$\mathsf{T}$$\mathsf{T}$$\mathsf{F}$
$\mathsf{F}$$\mathsf{T}$$\mathsf{F}$$\mathsf{T}$$\mathsf{T}$$\mathsf{F}$$\mathsf{T}$
$\mathsf{F}$$\mathsf{F}$$\mathsf{T}$$\mathsf{T}$$\mathsf{F}$$\mathsf{T}$$\mathsf{F}$
$\mathsf{F}$$\mathsf{F}$$\mathsf{F}$$\mathsf{T}$$\mathsf{F}$$\mathsf{T}$$\mathsf{F}$