# Boolean logic truth tables

- Human page: https://happytails.ai/en/calculators/boolean-logic-truth-tables/
- Markdown: https://happytails.ai/en/calculators/boolean-logic-truth-tables.md
- Structured JSON: https://happytails.ai/agents/en/calculators/boolean-logic-truth-tables/index.json
- Visibility: public

## Tool capabilities

| Property | Value |
| --- | --- |
| Tool ID | `boolean-logic-truth-tables` |
| Category | calculators |
| Implementation | Registered implementation. Registration alone is not a production-quality guarantee. |
| Browser execution | Automatic updates after valid input or file selection. |
| Browser processing | Browser; see tool notes for network behavior. |
| HTTP API | Not callable through HTTP. |
| Browser-agent interface | run_current_tool |

### Implementation notes

One formula per line, up to eight. Use not/!, and/&, xor/^, or/|, -> for implication and <-> for equivalence. Precedence follows that order. Parentheses override it; implication associates to the right. Variables are case-sensitive ASCII names. Up to 12 variables and 4,096 rows; no input code is executed.

### Inputs and settings

Text input: Logical formulas.

Example or placeholder shown in the interface (not a validated fixture):

```text
A -> B
not A or B
```

One formula per line. Use parentheses, Boolean operators and case-sensitive variables. Results update as you type. Up to 12,000 characters.

No additional settings are declared for this tool.

### Browser-agent workflow

1. Open the human page in a browser that supports WebMCP.
2. Discover the interface exposed by that page; use its actual schema.
3. Select files on the page first when the tool requires files.
4. Call `run_current_tool` with valid input and settings.
5. Inspect the returned result or error and the displayed output. Retrieve files from the displayed download links.

Calls do not automatically copy or download results. Browser permissions still apply. Interface availability alone is not proof of successful execution.

### Planning specification

One to eight formulas, one per line, using at most 12,000 characters. Use up to 12 case-sensitive ASCII variables, 512 tokens per formula and 64 nested operations. All assignments are enumerated, with one row for a constant formula. Supported operators: NOT, AND, XOR, OR, implication and equivalence, in that precedence order. Implication associates to the right. No input code is executed.

This describes intended requirements. Use the implementation notes, interface schema and observed output to determine current support.

### Complete machine-readable capability record

```json
{
  "id": "boolean-logic-truth-tables",
  "category": "calculators",
  "built": true,
  "requirements": "One to eight formulas, one per line, using at most 12,000 characters. Use up to 12 case-sensitive ASCII variables, 512 tokens per formula and 64 nested operations. All assignments are enumerated, with one row for a constant formula. Supported operators: NOT, AND, XOR, OR, implication and equivalence, in that precedence order. Implication associates to the right. No input code is executed.",
  "implementation": {
    "fields": [],
    "live": true,
    "background": true,
    "inputMaxLength": 12000,
    "inputErrorCode": "LOGIC_INPUT",
    "note": "One formula per line, up to eight. Use not/!, and/&, xor/^, or/|, -> for implication and <-> for equivalence. Precedence follows that order. Parentheses override it; implication associates to the right. Variables are case-sensitive ASCII names. Up to 12 variables and 4,096 rows; no input code is executed.",
    "experience": {
      "automatic": true,
      "single": false,
      "inputMaxLength": 12000,
      "inputMode": "text",
      "label": "Logical formulas",
      "placeholder": "A -> B\nnot A or B",
      "help": "One formula per line. Use parentheses, Boolean operators and case-sensitive variables. Results update as you type. Up to 12,000 characters.",
      "action": null
    },
    "mode": "automatic",
    "interactive": false
  },
  "execution": "Browser interface",
  "api": null,
  "browser_agent": {
    "supported": true,
    "name": "run_current_tool",
    "discovery": "WebMCP on the human page in a supporting browser",
    "verification": "See audit/API-AUDIT.md; availability is not verification"
  }
}
```

## Page guide

Build complete truth tables, classify formulas and compare logical equivalence with counterexamples.

How can we improve this tool?

Report a problem or share an idea.

Please leave out private information. Your message and the tool name go to our team via PostHog.

### How to use Boolean logic truth tables

1. Enter a formula on each line. Use parentheses to make the intended grouping clear.
2. Read the complete truth table. T means true and F means false.
3. Read classifications and equivalence checks in the report. For a non-equivalent pair, inspect its counterexample.

## Useful next steps

- [Continued fraction explorer](https://happytails.ai/en/calculators/continued-fraction-explorer/) ([Markdown](https://happytails.ai/en/calculators/continued-fraction-explorer.md))

- [Finite difference table explorer](https://happytails.ai/en/calculators/finite-difference-table-explorer/) ([Markdown](https://happytails.ai/en/calculators/finite-difference-table-explorer.md))

## What the result shows

A tautology is true for every assignment. A contradiction is false for every assignment. Other formulas are contingent. Equivalent formulas agree on every assignment to their combined variables.

### Operator order

NOT binds before AND, then XOR, OR, implication and equivalence. Use parentheses when in doubt. Variables such as A and a are different; true, false, 1 and 0 are constants.

### Keep the full result

CSV contains every assignment; JSON includes classifications and exact counterexamples. The text report explains the formula labels. Processing stays on your device.