Logic Truth Table: Answers Checked

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SUMMARY

The forum discussion centers on verifying the correctness of a logic truth table involving three variables: p, q, and r. The table evaluates expressions such as (p ∨ q) ∧ (q ∨ r), (¬p ∧ q) ∨ (p ∧ ¬r), and p → q → r. The consensus confirms that all answers are accurate except for one specific case, which requires further analysis to identify the discrepancy. Participants utilized logical operators and truth values to arrive at their conclusions.

PREREQUISITES
  • Understanding of logical operators (AND, OR, NOT)
  • Familiarity with truth tables and their construction
  • Knowledge of implications in logic (→)
  • Basic skills in logical reasoning and analysis
NEXT STEPS
  • Review the principles of constructing truth tables for complex expressions
  • Study logical equivalences and their applications in truth tables
  • Explore the implications of nested logical expressions
  • Practice with additional examples of truth tables involving multiple variables
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Students of logic, educators teaching logical reasoning, and anyone interested in understanding the fundamentals of truth tables and logical expressions.

Hotsuma
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Dear All,

Having trouble with a seemingly simple logic truth table. Are these answers correct?

\begin{tabular}{| c | c | c | c | c | c |}<br /> \hline<br /> p &amp; q &amp; r &amp; (p \vee q)\wedge(q \vee r) &amp; (\neg p \wedge q) \vee ( p \wedge \neg r) &amp; p \rightarrow q \rightarrow r\\<br /> \hline<br /> T &amp; T &amp; T &amp; T &amp; F &amp; T \\<br /> T &amp; T &amp; F &amp; T &amp; T &amp; F \\<br /> T &amp; F &amp; T &amp; T &amp; F &amp; T \\<br /> T &amp; F &amp; F &amp; F &amp; T &amp; F \\<br /> F &amp; T &amp; T &amp; T &amp; T &amp; T \\<br /> F &amp; T &amp; F &amp; T &amp; T &amp; F \\<br /> F &amp; F &amp; T &amp; F &amp; F &amp; T \\<br /> F &amp; F &amp; F &amp; F &amp; F &amp; T \\<br /> \hline<br /> \end{tabular}
 
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