Math / Building Blocks

The Grammar of Proof

Logic helps you say exactly what a rule permits and what would contradict it. Proof shows how a claim follows from stated assumptions.

Proposition

A statement that is true or false: “the bell is available.” Connectives such as and, or, and not combine statements.

Quantifier

A word that sets the reach of a claim: “every cue is silent” differs from “there is a silent cue.” One noisy cue defeats the first claim.

Set and function

A set collects things. A function assigns exactly one output to each input in its domain. These become useful when you represent the cues and decide which can play.

Try the rule on three props, or continue to the reference books below.

You are planning a tiny show in a room that needs quiet. There are three cue cards: a bell that is ready but makes sound, a lantern that is ready and silent, and a silent ribbon that is still missing.

Rule: a cue may play only when it is available and known to be silent. The lantern passes; the bell fails the sound condition; the ribbon fails the availability condition.

1. Write the two conditions on your cue sheet. Check each prop against both.
2. Replace and with or. Find a prop the new rule would admit by mistake.
3. Bring the ribbon back. Predict which decision changes, and which should stay the same.

Keep: the rule, one allowed example, and one counterexample. Turn them into a program decision, then check the awkward cases. This rule decides eligibility; it cannot tell you whether the show is good.

Formal reasoning was developed in parallel in India and China, with different questions at the center.