complete the truth table for \sim q \
ightarrow (p \vee q).

\begin{array}{|c|c|c|c|c|}
\hline
p & q & \sim q & p \vee q & \sim q \
ightarrow (p \vee q) \\
\hline
t & t & f & ? & ? \\
\hline
t & f & t & ? & ? \\
\hline
f & t & f & ? & ? \\
\hline
f & f & t & ? & ? \\
\hline
\end{array}

Question

complete the truth table for \sim q \
ightarrow (p \vee q).

\begin{array}{|c|c|c|c|c|}
\hline
p & q & \sim q & p \vee q & \sim q \
ightarrow (p \vee q) \\
\hline
t & t & f & ? & ? \\
\hline
t & f & t & ? & ? \\
\hline
f & t & f & ? & ? \\
\hline
f & f & t & ? & ? \\
\hline
\end{array}

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "table_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [], "current_concepts": [ "Truth Tables", "Logical Operators", "Conditional Statements" ] } ## Evaluate the disjunction column $p \lor q$ $$ \begin{aligned} &\text{Row 1: } \text{T} \lor \text{T} \equiv \text{T} \ &\text{Row 2: } \text{T} \lor \text{F} \equiv \text{T} \ &\text{Row 3: } \text{F} \lor \text{T} \equiv \text{T} \ &\text{Row 4: } \text{F} \lor \text{F} \equiv \text{F} \end{aligned} $$ ## Evaluate the conditional column $\sim q ightarrow (p \lor q)$ $$ \begin{aligned} &\text{Row 1: } \text{F} ightarrow \text{T} \equiv \text{T} \ &\text{Row 2: } \text{T} ightarrow \text{T} \equiv \text{T} \ &\text{Row 3: } \text{F} ightarrow \text{T} \equiv \text{T} \ &\text{Row 4: } \text{T} ightarrow \text{F} \equiv \text{F} \end{aligned} $$ | $p$ | $q$ | $\sim q$ | $p \lor q$ | $\sim q ightarrow (p \lor q)$ | |---|---|---|---|---| | T | T | F | T | T | | T | F | T | T | T | | F | T | F | T | T | | F | F | T | F | F | { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Truth Tables" ] }

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QUESTION IMAGE

Question

Explanation:

Evaluate the disjunction column \(p \lor q\)

Evaluate the conditional column \(\sim q

Answer: