Practice question · Numerical answer
How many rows does a truth table need for a sentence containing 5 distinct atomic propositions?
Hints
- Each atom doubles the number of rows.
- Compute 2 to the power 5.
Show the answer
32
Why
rows. The exponential growth is the whole reason natural deduction was developed, truth tables always work but stop being usable well before interesting arguments get large.
Practise Truth Tables
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More questions on Truth Tables
- 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.
- 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.