A → B — truth table
introonly row A=1, B=0 is false
Answer
4 rows, 3 true (0, 1, 3)
Why this example is worth doing
Material implication, and the row that every student queries: A = 0, B = 1 evaluates to true. The page explains that A → B claims nothing at all when A is false, so a false antecedent cannot make the implication false — it is a promise that has not been broken rather than one that has been kept. It also gives the equivalence A → B = Ā + B, which converts the whole discipline of propositional logic into ordinary Boolean algebra and lets every other tool on the site accept implications.
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 | A → B |
|---|---|---|---|
| 0 | 0 | 0 | 1 |
| 1 | 0 | 1 | 1 |
| 2 | 1 | 0 | 0 |
| 3 | 1 | 1 | 1 |