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Mathematical Logic
Turn statements into rules that can be checked step by step.
Follow the mechanism1 / 3
Claims receive truth values. A proposition can be tested as true or false, which gives reasoning a precise input instead of an impression.
propositional logicp → q · false
Focus the rule
Evaluate the compound statementp → qfalse
| p | q | p → q |
|---|---|---|
| T | T | T |
| T | F | F |
| F | T | T |
| F | F | T |
active row2 / 4
true rows3 / 4
p valueT
q valueF
This is the counterexample row: p is true but q is false, so the promise ‘if p, then q’ fails.
Truth tables enumerate every possible input row. They turn an argument into something checkable: a compound statement is valid only when its rule gives the intended result for every relevant assignment.