Truth Tables — Propositional Semantics

Quick Reference

Syntax (ASCII or Unicode)

Symbol	ASCII	Unicode
Negation	`~` or `-`	`¬`
Conjunction	`&` or `/\`	`∧`
Disjunction	`\|` or `\/`	`∨`
Conditional	`->` or `=>`	`→`
Biconditional	`<->`	`↔` (abbreviation)

Sentence letters: p, q, r, s, t, u, v, w

↔ is treated as an abbreviation for (φ→ψ)∧(ψ→φ)

How to use

Formulas card — enter one or more propositional formulas. Use Add formula for multiple. Examples show common patterns.
Build card — type a single formula and construct its truth table by clicking cells. Sentence-letter columns are pre-filled. Click each ? to cycle T → F → blank. Hit Check to verify your answers.
Check card — checks all formulas from the Formulas card for consistency. Consistent: highlights every row where all formulas are simultaneously true. Inconsistent: no such row exists.

Column order

Sentence letters (leftmost alternates slowest) · subformulas (depth-first) · main connective (highlighted in amber)

Formulas

Examples

Build

Type a formula above, then fill in the table that appears below.

Examples

Check

Checks the formulas in the Formulas card for consistency. A consistent set has at least one row where every formula is true simultaneously.