((A → B)·(B → C)) → (A → C) — truth table
coretautology: all 8 rows true
Answer
8 rows, 8 true (0, 1, 2, 3, 4, 5, 6, 7)
Why this example is worth doing
Hypothetical syllogism, and the first example on the page whose output column is constant. A tautology is how you prove an argument valid: build the implication from premises to conclusion and show it cannot be false. The tool labels the result as a tautology rather than leaving the reader to scan eight rows, and reports the same for contradictions and contingencies. This is the propositional-logic use of the truth table generator, which is a different search intent from the digital-logic one.
Try your own input in the Truth table generator. Turn an expression into a full truth table, with a column for every sub-expression.
How the answer is reached
Truth table
| # | A | B | C | (A → B) · (B → C) → A → C |
|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 1 | 1 |
| 2 | 0 | 1 | 0 | 1 |
| 3 | 0 | 1 | 1 | 1 |
| 4 | 1 | 0 | 0 | 1 |
| 5 | 1 | 0 | 1 | 1 |
| 6 | 1 | 1 | 0 | 1 |
| 7 | 1 | 1 | 1 | 1 |