Practice question · Put in order
Arrange the steps of building a truth table in order.
- Identify the distinct atomic propositions
- Work outward to the main connective
- Compute the columns for the smallest subformulas
- Read the sentence’s value from the main connective column
- Write 2 to the power n rows covering every combination
Hints
- The number of rows cannot be fixed before the atoms are counted.
- Compound columns are built from simpler ones, so the innermost come first.
Show the answer
- Identify the distinct atomic propositions
- Write 2 to the power n rows covering every combination
- Compute the columns for the smallest subformulas
- Work outward to the main connective
- Read the sentence’s value from the main connective column
Why
The order is forced by dependency: rows need the atom count, and each compound column needs its subformulas. The main connective column is the sentence’s own, reading the wrong column is a common slip.
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.
- 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.