a. complete the truth table for the compound statement: $p \lor \sim q$

\begin{array}{|c|c|c|c|}
\hline
p & q & \sim q & p \lor \sim q \\
\hline
t & t & ? & ? \\
\hline
t & f & ? & ? \\
\hline
f & t & ? & ? \\
\hline
f & f & ? & ? \\
\hline
\end{array}

b. complete the truth table for the compound statement: $\sim p \land \sim q$

\begin{array}{|c|c|c|c|c|}
\hline
p & q & \sim p & \sim q & \sim p \land \sim q \\
\hline
t & t & ? & ? & ? \\
\hline
t & f & ? & ? & ? \\
\hline
f & t & ? & ? & ? \\
\hline
f & f & ? & ? & ? \\
\hline
\end{array}

Question

a. complete the truth table for the compound statement: $p \lor \sim q$

\begin{array}{|c|c|c|c|}
\hline
p & q & \sim q & p \lor \sim q \\
\hline
t & t & ? & ? \\
\hline
t & f & ? & ? \\
\hline
f & t & ? & ? \\
\hline
f & f & ? & ? \\
\hline
\end{array}

b. complete the truth table for the compound statement: $\sim p \land \sim q$

\begin{array}{|c|c|c|c|c|}
\hline
p & q & \sim p & \sim q & \sim p \land \sim q \\
\hline
t & t & ? & ? & ? \\
\hline
t & f & ? & ? & ? \\
\hline
f & t & ? & ? & ? \\
\hline
f & f & ? & ? & ? \\
\hline
\end{array}

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "table_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Truth Tables", "Logical Operators", "Truth Table Construction" ], "new_concepts": [], "current_concepts": [ "Truth Tables", "Logical Operators", "Truth Table Construction" ] } ## Evaluate negation columns $$ \begin{aligned} &\sim p: \text{negates } p \implies \text{maps } (T, T, F, F) \to (F, F, T, T)\ &\sim q: \text{negates } q \implies \text{maps } (T, F, T, F) \to (F, T, F, T) \end{aligned} $$ ## Evaluate disjunction column for part a $$ \begin{aligned} &p \lor \sim q \text{ is False only when both } p \text{ and } \sim q \text{ are False:}\ &\text{Row 1: } T \lor F = T\ &\text{Row 2: } T \lor T = T\ &\text{Row 3: } F \lor F = F\ &\text{Row 4: } F \lor T = T \end{aligned} $$ ## Evaluate conjunction column for part b $$ \begin{aligned} &\sim p \land \sim q \text{ is True only when both } \sim p \text{ and } \sim q \text{ are True:}\ &\text{Row 1: } F \land F = F\ &\text{Row 2: } F \land T = F\ &\text{Row 3: } T \land F = F\ &\text{Row 4: } T \land T = T \end{aligned} $$ ## Question a | $p$ | $q$ | $\sim q$ | $p \lor \sim q$ | |---|---|---|---| | T | T | F | T | | T | F | T | T | | F | T | F | F | | F | F | T | T | ## Question b | $p$ | $q$ | $\sim p$ | $\sim q$ | $\sim p \land \sim q$ | |---|---|---|---|---| | T | T | F | F | F | | T | F | F | T | F | | F | T | T | F | F | | F | F | T | T | T | { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Truth Tables" ] }

\(p\)	\(q\)	\(\sim q\)	\(p \lor \sim q\)
T	F	T	T
F	T	F	F
F	F	T	T

\(p\)	\(q\)	\(\sim p\)	\(\sim q\)	\(\sim p \land \sim q\)
T	F	F	T	F
F	T	T	F	F
F	F	T	T	T

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QUESTION IMAGE

Question

Explanation:

Evaluate negation columns

Evaluate disjunction column for part a

Evaluate conjunction column for part b

Answer:

Question a

Question b