You are the logic engine. An if-then statement is a promise, and a promise only lives in four possible worlds. Nothing on this page tells you the answers. Stand in a world, decide for yourself whether the promise and its three look-alike cousins hold, and type T or F into the table. A stamp appears on a card only once you have earned it.
symbols, beside their English at all times: → means "if … then" · ¬ means "not"
≡ the statement and its contrapositive get the same stamp in every world — logically equivalent
≡ the converse and the inverse always match each other — but not the statement
Fill every cell yourself. Type T or F, or tap the pad below. Arrow keys move between cells; a wrong answer is marked and stays open for another try.
0 of 16 cells earned
| P | Q | P→Q | ¬Q→¬P | Q→P | ¬P→¬Q |
|---|
All sixteen earned. Read down the columns: P→Q and ¬Q→¬P are identical; Q→P and ¬P→¬Q are identical to each other — a different pair.
Suppose the promise P → Q itself is trustworthy. Then a single new fact buys you exactly one deduction. Learning P is true pushes forward (modus ponens); learning Q is false pushes backward along the contrapositive ¬Q → ¬P (modus tollens).