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Write out the truth table for $\lnot \bigl[ \lnot \bigl( \lnot \left(P \Rightarrow Q\right)\bigr)\bigr]$.
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$$Q$$P \Rightarrow Q$$\lnot C_1$$ \lnot C_2$$\lnot C_3 \mathsf{T}$$\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}$$\mathsf{F}$$\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}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r1c3}}\hspace{35px}}~} \mathsf{F}$$\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{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}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r3c3}}\hspace{35px}}~} C_1$$C_2$$C_3 P$$Q$$P \Rightarrow Q$$ \lnot C_1$$\lnot C_2$$ \lnot C_3$
$\mathsf{T}$$\mathsf{T}$$\mathsf{T}$$\mathsf{F}$$\mathsf{T}$$\mathsf{F} \mathsf{T}$$\mathsf{F}$$\mathsf{F}$$\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}$