Practice question · Match the pairs
Match each truth-table result to what it establishes about an argument.
- No row has true premises and a false conclusion
- Some row has true premises and a false conclusion
- The conclusion is true in every row
- Premises and conclusion columns match exactly
- That row is a counterexample
- The conclusion is a tautology
- They are logically equivalent
- The argument is valid
Hints
- Validity is the absence of one specific kind of row.
- A single bad row is enough to refute an argument.
Show the answer
- No row has true premises and a false conclusion → The argument is valid
- Some row has true premises and a false conclusion → That row is a counterexample
- The conclusion is true in every row → The conclusion is a tautology
- Premises and conclusion columns match exactly → They are logically equivalent
Why
Validity is established by exhausting the possibilities and finding no counterexample. One bad row refutes; no bad rows prove. This asymmetry, one counterexample suffices, runs through all of logic.
Practise Truth Tables
The app has 3 more questions on this lesson, and keeps your place in the course. Philosophy I is free to start.
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.
- Propositional logic is termed decidable because truth tables offer an exhaustive decision procedure. What…
- Which are correct statements of De Morgan’s laws?
- A sentence contains 4 distinct atomic propositions. Set the number of rows its truth table requires.