Question

complete the truth table for the compound statement: \\(a \lor (b \land c)\\).

you will probably want to complete the intermediate columns on your own paper and then enter the final answer in the truth table.

\\(\

$$\begin{array}{|c|c|c|c|} \\hline a & b & c & a \\lor (b \\land c) \\\\ \\hline t & t & t & ? \\\\ \\hline t & t & f & ? \\\\ \\hline t & f & t & ? \\\\ \\hline t & f & f & ? \\\\ \\hline f & t & t & ? \\\\ \\hline f & t & f & ? \\\\ \\hline f & f & t & ? \\\\ \\hline f & f & f & ? \\\\ \\hline \\end{array}$$

\\)

Explanation:

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<reasoning>

Evaluate the conjunction \(B \land C\)

\[

$$\begin{array}{ccc|c} A & B & C & B \land C \\ \hline \text{T} & \text{T} & \text{T} & \text{T} \\ \text{T} & \text{T} & \text{F} & \text{F} \\ \text{T} & \text{F} & \text{T} & \text{F} \\ \text{T} & \text{F} & \text{F} & \text{F} \\ \text{F} & \text{T} & \text{T} & \text{T} \\ \text{F} & \text{T} & \text{F} & \text{F} \\ \text{F} & \text{F} & \text{T} & \text{F} \\ \text{F} & \text{F} & \text{F} & \text{F} \end{array}$$

\]

Evaluate the disjunction \(A \lor (B \land C)\)

\[

$$\begin{array}{ccc|c|c} A & B & C & B \land C & A \lor (B \land C) \\ \hline \text{T} & \text{T} & \text{T} & \text{T} & \text{T} \\ \text{T} & \text{T} & \text{F} & \text{F} & \text{T} \\ \text{T} & \text{F} & \text{T} & \text{F} & \text{T} \\ \text{T} & \text{F} & \text{F} & \text{F} & \text{T} \\ \text{F} & \text{T} & \text{T} & \text{T} & \text{T} \\ \text{F} & \text{T} & \text{F} & \text{F} & \text{F} \\ \text{F} & \text{F} & \text{T} & \text{F} & \text{F} \\ \text{F} & \text{F} & \text{F} & \text{F} & \text{F} \end{array}$$

\]
</reasoning>

<answer>
Complete the truth table for the compound statement: \(A \lor (B \land C)\).

\(A\)	\(B\)	\(C\)	\(A \lor (B \land C)\)
T	T	F	<blank>T</blank>
T	F	T	<blank>T</blank>
T	F	F	<blank>T</blank>
F	T	T	<blank>T</blank>
F	T	F	<blank>F</blank>
F	F	T	<blank>F</blank>
F	F	F	<blank>F</blank>

</answer>

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Answer:

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<reasoning>

Evaluate the conjunction \(B \land C\)

\[

$$\begin{array}{ccc|c} A & B & C & B \land C \\ \hline \text{T} & \text{T} & \text{T} & \text{T} \\ \text{T} & \text{T} & \text{F} & \text{F} \\ \text{T} & \text{F} & \text{T} & \text{F} \\ \text{T} & \text{F} & \text{F} & \text{F} \\ \text{F} & \text{T} & \text{T} & \text{T} \\ \text{F} & \text{T} & \text{F} & \text{F} \\ \text{F} & \text{F} & \text{T} & \text{F} \\ \text{F} & \text{F} & \text{F} & \text{F} \end{array}$$

\]

Evaluate the disjunction \(A \lor (B \land C)\)

\[

$$\begin{array}{ccc|c|c} A & B & C & B \land C & A \lor (B \land C) \\ \hline \text{T} & \text{T} & \text{T} & \text{T} & \text{T} \\ \text{T} & \text{T} & \text{F} & \text{F} & \text{T} \\ \text{T} & \text{F} & \text{T} & \text{F} & \text{T} \\ \text{T} & \text{F} & \text{F} & \text{F} & \text{T} \\ \text{F} & \text{T} & \text{T} & \text{T} & \text{T} \\ \text{F} & \text{T} & \text{F} & \text{F} & \text{F} \\ \text{F} & \text{F} & \text{T} & \text{F} & \text{F} \\ \text{F} & \text{F} & \text{F} & \text{F} & \text{F} \end{array}$$

\]
</reasoning>

<answer>
Complete the truth table for the compound statement: \(A \lor (B \land C)\).

\(A\)	\(B\)	\(C\)	\(A \lor (B \land C)\)
T	T	F	<blank>T</blank>
T	F	T	<blank>T</blank>
T	F	F	<blank>T</blank>
F	T	T	<blank>T</blank>
F	T	F	<blank>F</blank>
F	F	T	<blank>F</blank>
F	F	F	<blank>F</blank>

</answer>

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