Practice question · Multiple choice
Propositional logic is termed decidable because truth tables offer an exhaustive decision procedure. What does this exhaustive quality guarantee when evaluating an argument?
Hints
- Does listing every truth-value combination leave room for an indeterminate result?
- What is the difference between a semantic valuation procedure and a syntactic proof system?
Show the answer
A. A mechanical guarantee of reaching a definitive verdict
Why
Decidability ensures a definitive semantic result via finite valuation, not syntactic derivation or false-free premises. Finding invalidity requires only one counterexample row, while syntactic methods like natural deduction bypass truth tables entirely.
Practise Truth Tables
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More questions on Truth Tables
- How many rows does a truth table need for a sentence containing 5 distinct atomic propositions?
- Why does the exponential growth of truth tables motivate natural deduction?
- Two sentences count as logically equivalent as soon as their truth-table columns agree in at least one row.
- Arrange the steps of building a truth table in order.
- Which are correct statements of De Morgan’s laws?
- Match each truth-table result to what it establishes about an argument.
- A sentence contains 4 distinct atomic propositions. Set the number of rows its truth table requires.