Problem

\begin{tabular}{|c|c|c|r|}
\hline $\mathrm{A}$ & $\mathrm{B}$ & $\mathrm{C}$ & $(\mathrm{A} \wedge \mathrm{B}) \vee \mathrm{C}$ \\
\hline $\mathrm{T}$ & $\mathrm{T}$ & $\mathrm{T}$ & $? \mathrm{~V}$ \\
\hline $\mathrm{T}$ & $\mathrm{T}$ & $\mathrm{F}$ & $? \vee$ \\
\hline $\mathrm{T}$ & $\mathrm{F}$ & $\mathrm{T}$ & $? \vee$ \\
\hline $\mathrm{T}$ & $\mathrm{F}$ & $\mathrm{F}$ & $? \vee$ \\
\hline $\mathrm{F}$ & $\mathrm{T}$ & $\mathrm{T}$ & $? \vee$ \\
\hline $\mathrm{F}$ & $\mathrm{T}$ & $\mathrm{F}$ & $? \vee$ \\
\hline $\mathrm{F}$ & $\mathrm{F}$ & $\mathrm{T}$ & $? \vee$ \\
\hline $\mathrm{F}$ & $\mathrm{F}$ & $\mathrm{F}$ & $? \vee$ \\
\hline
\end{tabular}

Answer

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Answer

Fill in the missing values in the table.

Steps

Step 1 :Evaluate the expression \((A \land B) \lor C\) for each combination of truth values for \(A\), \(B\), and \(C\).

Step 2 :For the first row, \(A = T\), \(B = T\), \(C = T\). Evaluate \((A \land B) \lor C\). Since \(A \land B\) is true and \(C\) is true, the expression evaluates to true. Therefore, the missing value is \(T\).

Step 3 :For the second row, \(A = T\), \(B = T\), \(C = F\). Evaluate \((A \land B) \lor C\). Since \(A \land B\) is true and \(C\) is false, the expression evaluates to true. Therefore, the missing value is \(T\).

Step 4 :For the third row, \(A = T\), \(B = F\), \(C = T\). Evaluate \((A \land B) \lor C\). The expression evaluates to false. Therefore, the missing value is \(F\).

Step 5 :For the fourth row, \(A = T\), \(B = F\), \(C = F\). Evaluate \((A \land B) \lor C\). The expression evaluates to false. Therefore, the missing value is \(F\).

Step 6 :For the fifth row, \(A = F\), \(B = T\), \(C = T\). Evaluate \((A \land B) \lor C\). The expression evaluates to true. Therefore, the missing value is \(T\).

Step 7 :For the sixth row, \(A = F\), \(B = T\), \(C = F\). Evaluate \((A \land B) \lor C\). The expression evaluates to false. Therefore, the missing value is \(F\).

Step 8 :For the seventh row, \(A = F\), \(B = F\), \(C = T\). Evaluate \((A \land B) \lor C\). The expression evaluates to true. Therefore, the missing value is \(T\).

Step 9 :For the eighth row, \(A = F\), \(B = F\), \(C = F\). Evaluate \((A \land B) \lor C\). The expression evaluates to false. Therefore, the missing value is \(F\).

Step 10 :Fill in the missing values in the table.

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