Formulaic Maths Problems - get another problem: level 1, level 2, level 3 - link to this problem
Write out the truth table for $\bigl[\bigl(\left(P \lor P\right) \Rightarrow R\bigr) \lor S\bigr] \land \bigl(Q \Leftrightarrow \left(S \oplus S\right)\bigr)$.
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$$C_4$$C_5$
$P$$Q$$R$$S$$P \lor P$$C_1 \Rightarrow R$$C_2 \lor S$$S \oplus S$$Q \Leftrightarrow C_4$$C_3 \land C_5 \mathsf{T}$$\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}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r0c4}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r0c5}}\hspace{35px}}~}$
$\mathsf{T}$$\mathsf{T}$$\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}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r1c3}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r1c4}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r1c5}}\hspace{35px}}~} \mathsf{T}$$\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}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r2c4}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r2c5}}\hspace{35px}}~}$
$\mathsf{T}$$\mathsf{T}$$\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}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r3c3}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r3c4}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r3c5}}\hspace{35px}}~} \mathsf{T}$$\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}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r4c4}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r4c5}}\hspace{35px}}~}$
$\mathsf{T}$$\mathsf{F}$$\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}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r5c3}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r5c4}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r5c5}}\hspace{35px}}~} \mathsf{T}$$\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}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r6c4}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r6c5}}\hspace{35px}}~}$
$\mathsf{T}$$\mathsf{F}$$\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}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r7c3}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r7c4}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r7c5}}\hspace{35px}}~} \mathsf{F}$$\mathsf{T}$$\mathsf{T}$$\mathsf{T}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r8c0}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r8c1}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r8c2}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r8c3}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r8c4}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r8c5}}\hspace{35px}}~}$
$\mathsf{F}$$\mathsf{T}$$\mathsf{T}$$\mathsf{F}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r9c0}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r9c1}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r9c2}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r9c3}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r9c4}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r9c5}}\hspace{35px}}~} \mathsf{F}$$\mathsf{T}$$\mathsf{F}$$\mathsf{T}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r10c0}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r10c1}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r10c2}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r10c3}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r10c4}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r10c5}}\hspace{35px}}~}$
$\mathsf{F}$$\mathsf{T}$$\mathsf{F}$$\mathsf{F}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r11c0}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r11c1}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r11c2}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r11c3}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r11c4}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r11c5}}\hspace{35px}}~} \mathsf{F}$$\mathsf{F}$$\mathsf{T}$$\mathsf{T}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r12c0}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r12c1}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r12c2}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r12c3}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r12c4}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r12c5}}\hspace{35px}}~}$
$\mathsf{F}$$\mathsf{F}$$\mathsf{T}$$\mathsf{F}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r13c0}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r13c1}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r13c2}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r13c3}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r13c4}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r13c5}}\hspace{35px}}~} \mathsf{F}$$\mathsf{F}$$\mathsf{F}$$\mathsf{T}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r14c0}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r14c1}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r14c2}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r14c3}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r14c4}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r14c5}}\hspace{35px}}~}$
$\mathsf{F}$$\mathsf{F}$$\mathsf{F}$$\mathsf{F}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r15c0}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r15c1}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r15c2}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r15c3}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r15c4}}\hspace{35px}}~}$$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{r15c5}}\hspace{35px}}~} C_1$$C_2$$C_3$$C_4$$C_5 P$$Q$$R$$S$$P \lor P$$C_1 \Rightarrow R$$C_2 \lor S$$S \oplus S$$Q \Leftrightarrow C_4$$C_3 \land C_5$
$\mathsf{T}$$\mathsf{T}$$\mathsf{T}$$\mathsf{T}$$\mathsf{T}$$\mathsf{T}$$\mathsf{T}$$\mathsf{F}$$\mathsf{F}$$\mathsf{F} \mathsf{T}$$\mathsf{T}$$\mathsf{T}$$\mathsf{F}$$\mathsf{T}$$\mathsf{T}$$\mathsf{T}$$\mathsf{F}$$\mathsf{F}$$\mathsf{F}$
$\mathsf{T}$$\mathsf{T}$$\mathsf{F}$$\mathsf{T}$$\mathsf{T}$$\mathsf{F}$$\mathsf{T}$$\mathsf{F}$$\mathsf{F}$$\mathsf{F} \mathsf{T}$$\mathsf{T}$$\mathsf{F}$$\mathsf{F}$$\mathsf{T}$$\mathsf{F}$$\mathsf{F}$$\mathsf{F}$$\mathsf{F}$$\mathsf{F}$
$\mathsf{T}$$\mathsf{F}$$\mathsf{T}$$\mathsf{T}$$\mathsf{T}$$\mathsf{T}$$\mathsf{T}$$\mathsf{F}$$\mathsf{T}$$\mathsf{T} \mathsf{T}$$\mathsf{F}$$\mathsf{T}$$\mathsf{F}$$\mathsf{T}$$\mathsf{T}$$\mathsf{T}$$\mathsf{F}$$\mathsf{T}$$\mathsf{T}$
$\mathsf{T}$$\mathsf{F}$$\mathsf{F}$$\mathsf{T}$$\mathsf{T}$$\mathsf{F}$$\mathsf{T}$$\mathsf{F}$$\mathsf{T}$$\mathsf{T} \mathsf{T}$$\mathsf{F}$$\mathsf{F}$$\mathsf{F}$$\mathsf{T}$$\mathsf{F}$$\mathsf{F}$$\mathsf{F}$$\mathsf{T}$$\mathsf{F}$
$\mathsf{F}$$\mathsf{T}$$\mathsf{T}$$\mathsf{T}$$\mathsf{F}$$\mathsf{T}$$\mathsf{T}$$\mathsf{F}$$\mathsf{F}$$\mathsf{F} \mathsf{F}$$\mathsf{T}$$\mathsf{T}$$\mathsf{F}$$\mathsf{F}$$\mathsf{T}$$\mathsf{T}$$\mathsf{F}$$\mathsf{F}$$\mathsf{F}$
$\mathsf{F}$$\mathsf{T}$$\mathsf{F}$$\mathsf{T}$$\mathsf{F}$$\mathsf{T}$$\mathsf{T}$$\mathsf{F}$$\mathsf{F}$$\mathsf{F} \mathsf{F}$$\mathsf{T}$$\mathsf{F}$$\mathsf{F}$$\mathsf{F}$$\mathsf{T}$$\mathsf{T}$$\mathsf{F}$$\mathsf{F}$$\mathsf{F}$
$\mathsf{F}$$\mathsf{F}$$\mathsf{T}$$\mathsf{T}$$\mathsf{F}$$\mathsf{T}$$\mathsf{T}$$\mathsf{F}$$\mathsf{T}$$\mathsf{T} \mathsf{F}$$\mathsf{F}$$\mathsf{T}$$\mathsf{F}$$\mathsf{F}$$\mathsf{T}$$\mathsf{T}$$\mathsf{F}$$\mathsf{T}$$\mathsf{T}$
$\mathsf{F}$$\mathsf{F}$$\mathsf{F}$$\mathsf{T}$$\mathsf{F}$$\mathsf{T}$$\mathsf{T}$$\mathsf{F}$$\mathsf{T}$$\mathsf{T} \mathsf{F}$$\mathsf{F}$$\mathsf{F}$$\mathsf{F}$$\mathsf{F}$$\mathsf{T}$$\mathsf{T}$$\mathsf{F}$$\mathsf{T}$$\mathsf{T}$