Mathematical Logic:
the grammar of certainty.
Before graphs, groups, or Boolean circuits — every proof, every algorithm, and every line of code you'll ever write rests on one skill: telling a true statement from a false one, precisely. Type any sentence below and see logic decide it.
Statements
A proposition is a declarative sentence that is either true or false — never both, never neither. Questions, commands, and opinions don't qualify because they carry no fixed truth value. Sort these six examples yourself before reading the rule below.
Connectives
Two propositions, p and q, can be combined into a compound statement. The connective you choose changes the entire truth table. Pick one and watch it build live.
Tautology & contradiction
Every compound statement falls into one of three buckets, decided by its truth table. A tautology is always true, a contradiction is always false, and a contingency is sometimes true, sometimes false. Classify each expression — the table above will help if you want to work it out by hand first.
The laws
These identities let you rewrite one logical expression as another, equivalent one — the algebra that every simplification and every circuit optimisation is built from. Tap a card to reveal the identity.
Quantifiers
A statement like "x is even" isn't a proposition on its own — it's a predicate, waiting for x to be filled in. Quantifiers turn predicates back into propositions by saying how many values of x make it true. Click numbers in and out of the domain and watch both readouts update.
Where this shows up
if statements and && / || operators in every programming language are propositional logic with different spelling. Database query filters (WHERE age > 18 AND city = 'Pune') are compound propositions. Digital circuits are truth tables built from wires. Mathematical proofs — the ones you'll write for the rest of this series on relations, graphs, groups, and Boolean algebra — are chains of propositions connected by ⇒ and justified line by line. Everything after this chapter assumes you can read a truth table without thinking twice.
Ten questions
No pressure, no timer. Get your score, see the reasoning, retry if you want. This gates nothing — it's just proof to yourself that the chapters above stuck.
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