(A + B) → C — truth table
core8 rows, 5 true
Answer
8 rows, 5 true (0, 1, 3, 5, 7)
Why this example is worth doing
A compound antecedent, which is where operator precedence starts to matter. This tool binds implication looser than every other connective, so A + B → C without brackets parses as (A + B) → C — but not every textbook agrees, and the wrong reading gives a different table. The page states the precedence order in force, warns when an input is ambiguous enough that another convention would change the result, and shows the fully parenthesised form of what it actually parsed.
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 → C |
|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 1 | 1 |
| 2 | 0 | 1 | 0 | 0 |
| 3 | 0 | 1 | 1 | 1 |
| 4 | 1 | 0 | 0 | 0 |
| 5 | 1 | 0 | 1 | 1 |
| 6 | 1 | 1 | 0 | 0 |
| 7 | 1 | 1 | 1 | 1 |