Math & Numbers

Venn Diagram Problem Solver (Set Cardinality)

2-set and 3-set inclusion-exclusion solver: every disjoint region, the union, and the outside count, with consistency checks.

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Quick start

Call this tool from your code in three languages.

cURL

curl -X POST 'http://127.0.0.1:3003/en/api/tools/venn-diagram-problem-solver' \
  -H 'Content-Type: application/json' \
  -d '{"problemType":"3","sizeA":40,"sizeB":35,"sizeC":45,"ab":15,"ac":18,"bc":12,"abc":8,"universe":100}'

API reference

Send a POST request with your inputs as JSON. File parameters require a separate upload first.

Endpoint

HTTP

POST http://127.0.0.1:3003/en/api/tools/venn-diagram-problem-solver

Parameters

Name	Type	Required	Description
problemType	select	Yes	—
sizeA	number	No	Number of elements in A.
sizeB	number	No	Number of elements in B.
sizeC	number	No	Number of elements in C (3-set problems).
ab	number	No	Elements in both A and B.

MCP integration

Add this tool to your Model Context Protocol server so AI agents can list and call it.

Server configuration

Add this block to your MCP client configuration:

mcp.json

{
  "mcpServers": {
    "elysiatools-venn-diagram-problem-solver": {
      "name": "venn-diagram-problem-solver",
      "description": "2-set and 3-set inclusion-exclusion solver: every disjoint region, the union, and the outside count, with consistency checks.",
      "baseUrl": "http://127.0.0.1:3003/mcp/sse?toolId=venn-diagram-problem-solver",
      "command": "",
      "args": [],
      "env": {},
      "isActive": true,
      "type": "sse"
    }
  }
}

List available tools

After connecting to the SSE endpoint, list the exposed tools:

tools/list

{
  "jsonrpc": "2.0",
  "id": 1,
  "method": "tools/list"
}

Call this tool

Invoke the tool by its id, passing arguments built from its parameters:

tools/call

{
  "jsonrpc": "2.0",
  "id": 2,
  "method": "tools/call",
  "params": {
    "name": "venn-diagram-problem-solver",
    "arguments": {
  "problemType": "3",
  "sizeA": 40,
  "sizeB": 35,
  "sizeC": 45,
  "ab": 15,
  "ac": 18,
  "bc": 12,
  "abc": 8,
  "universe": 100
}
  }
}

Chain multiple tools in one session with a comma-separated toolId list, e.g. /mcp/sse?toolId=png-to-webp,jpg-to-webp,gif-to-webp (max 20).

Questions or issues? Contact [email protected]

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