Practice question · Multiple choice
Why does the exponential growth of truth tables motivate natural deduction?
Hints
- The problem is practical rather than a failure of correctness.
- Twenty atoms need over a million rows, though each one would be right.
Show the answer
A. Tables remain correct but become impractically large for many atoms
Why
Tables never become wrong, they become unusable. A twenty-atom sentence needs over a million rows, all correct and none of them worth writing. Natural deduction reaches the same verdicts by following rules instead of exhausting cases.
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?
- 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.
- Propositional logic is termed decidable because truth tables offer an exhaustive decision procedure. What…
- 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.