Formulaic Maths Problems - get another problem: level 1, level 2, level 3 - link to this problem
Loading, please wait...
Write out the truth table for $\bigl(\left(P \lor Q\right) \Leftrightarrow \lnot Q\bigr) \Leftrightarrow Q$.
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 \lor Q$$ \lnot Q$$C_1 \Leftrightarrow C_2$$C_3 \Leftrightarrow Q$
$\mathsf{T}$$\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$$P \lor Q$$ \lnot Q$$C_1 \Leftrightarrow C_2$$C_3 \Leftrightarrow Q$
$\mathsf{T}$$\mathsf{T}$$\mathsf{T}$$\mathsf{F}$$\mathsf{F}$$\mathsf{F}$
$\mathsf{T}$$\mathsf{F}$$\mathsf{T}$$\mathsf{T}$$\mathsf{T}$$\mathsf{F}$
$\mathsf{F}$$\mathsf{T}$$\mathsf{T}$$\mathsf{F}$$\mathsf{F}$$\mathsf{F}$
$\mathsf{F}$$\mathsf{F}$$\mathsf{F}$$\mathsf{T}$$\mathsf{F}$$\mathsf{T}$