# Propositions & Connectives

Canonical: https://manyspace.aporia.systems/topics/propositions-connectives-mth-logic-086
Updated: 2026-10-13

Mathematics · Mathematical Logic · MTH-LOGIC-086

- Difficulty: 2 / 5
- Importance: 4 / 5
- Study time: 1.5–3 h

and, or, not, implies, iff; atomic vs compound statements

## Why it matters

Provides the precise language of mathematical statements and the rules of valid reasoning underlying all proofs.

## Where it is used

Formal verification, algorithm correctness, database queries, AI knowledge representation, clean reasoning in business decisions.

## How you know you have learned it

Explain from memory in your own words + answer 2 transfer questions correctly.

## What you need first

- [Complex Numbers](https://manyspace.aporia.systems/topics/complex-numbers-mth-alg2-051) (required)

## What it opens

- [Sets & Set Notation](https://manyspace.aporia.systems/topics/sets-set-notation-mth-sets-094)
- [Set Operations](https://manyspace.aporia.systems/topics/set-operations-mth-sets-095)
- [Set Algebra Laws](https://manyspace.aporia.systems/topics/set-algebra-laws-mth-sets-096)
- [Cartesian Products & Relations](https://manyspace.aporia.systems/topics/cartesian-products-relations-mth-sets-097)
- [Equivalence Relations](https://manyspace.aporia.systems/topics/equivalence-relations-mth-sets-098)
- [Partial Orders](https://manyspace.aporia.systems/topics/partial-orders-mth-sets-099)
- [Functions as Sets](https://manyspace.aporia.systems/topics/functions-as-sets-mth-sets-100)
- [Finite & Infinite Sets](https://manyspace.aporia.systems/topics/finite-infinite-sets-mth-sets-101)
- [Countable vs Uncountable](https://manyspace.aporia.systems/topics/countable-vs-uncountable-mth-sets-102)
- [Cantor's Theorem & Power Sets](https://manyspace.aporia.systems/topics/cantor-s-theorem-power-sets-mth-sets-103)
- [Direct Proof](https://manyspace.aporia.systems/topics/direct-proof-mth-proofs-104)
- [Proof by Contrapositive](https://manyspace.aporia.systems/topics/proof-by-contrapositive-mth-proofs-105)
- [Proof by Contradiction](https://manyspace.aporia.systems/topics/proof-by-contradiction-mth-proofs-106)
- [Mathematical Induction](https://manyspace.aporia.systems/topics/mathematical-induction-mth-proofs-107)
- [Strong Induction](https://manyspace.aporia.systems/topics/strong-induction-mth-proofs-108)
- [Existence & Uniqueness Proofs](https://manyspace.aporia.systems/topics/existence-uniqueness-proofs-mth-proofs-109)
- [Counterexamples & Disproof](https://manyspace.aporia.systems/topics/counterexamples-disproof-mth-proofs-110)
- [Proof Writing Craft](https://manyspace.aporia.systems/topics/proof-writing-craft-mth-proofs-111)

## Resources

- How to Prove It — Daniel Velleman