VectorPaint AND/OR/NOT cards: map four inputs to three outputs

English translation of the Chinese original, translated on 2026-11-07. Original publication dates, attribution, code and version notes are retained.

Here 0/1 mean false/true, not magnitude or priority. Manually map four combinations of propositions P/Q to NOT P, P AND Q and P OR Q. OR is inclusive—at least one true—not an everyday either-but-not-both reading. The app lays out the card; you evaluate/check it without automatic logical execution or proof.

Define inputs, outputs and the meaning of zero/one

Create a 1200 by 800 pixel canvas with input columns P/Q and outputs NOT P, P AND Q, P OR Q. Define 0 false/1 true and use abstract propositions, not judgements about groups. NOT P reverses P independently of Q; AND needs both true; OR needs at least one. Read these definitions before copying values. This specifies no voltage, programming type or approval policy and is not an implemented decision interface.

Make four complete, unique input rows

Use inputs 00,01,10,11 once each: two binary choices produce four cases. Inspect inputs alone for an omitted 10 or duplicate 01. Headers/row IDs are not cases. Keep P left/Q right; reordering later requires every explanation updated. Use clear consistent digits without colour dependence. Save input sources before output so anticipated results cannot distort the cases.

Evaluate NOT P from P alone

P is 0 in the first two rows, so NOT P is 1; the last two give 0, producing 1,1,0,0. Changing Q alone does not change NOT P. Do not negate both inputs and collapse them into one result. A short explanatory pointer must refer to P, not Q. Check this column with other outputs hidden, then restore. Negation is a defined value operation, not flipping glyphs or reversing colours; text colour does not automatically change logical meaning.

Check AND and OR separately before comparing

AND is true only on 11, yielding 0,0,0,1. OR is false only on 00, yielding 0,1,1,1. In particular, OR on 11 stays 1; writing 0 defines another rule, not inclusive OR. Audit columns separately before comparison and do not swap their positions. One text colour suffices; inconsistent green meanings should not replace headers/rules. Explain each result from its inputs before decoration.

Use one deliberate error to test the checking method

In a copy, change final-row OR to 0 with inputs/other results fixed. Apply at-least-one-true: 11 satisfies it, regardless of another zero elsewhere in the row. Restore the final source to 1. On 01, AND=0 and OR=1 answer different conditions without contradiction. This is neither automated error detection nor formal verification of complex propositions; it checks your ability to identify one error from explicit rules.

Keep formal cards separate from natural-language examples

Optional everyday examples must be low-risk, invented examples and must define P/Q explicitly without relying on unstated common sense. Natural-language or may be exclusive, so retain the inclusive convention. Changing an example need not change the abstract table but does require remapping proposition identities. Explaining a real decision process requires separately stated contextual conditions; this abstract card is not a completed workflow. Not every real-world sentence fits this two-input, five-column format. Save the abstract card before a separate example page can obscure its definitions.

Read inputs before three outputs in the export

Save rules, input source and complete card. In actual output, read P/Q before NOT/AND/OR per row, especially the last. Keep 0/1 and headings distinct; widen layout rather than deleting qualifications. Test text/lines on another background and handle real backing objects. Name inclusive-OR truth card, revision and size and exclude deliberate errors. Preserve field order for editable delivery and audit after rewording/reordering. Neither SVG nor raster output is an executable logic program.

Check for a changed rule when OR on eleven becomes zero

For final OR error, return to inclusive meaning instead of renaming the header vaguely. NOT changing with Q suggests the wrong input column; AND=1 on 10 violates both-true. Repeated cases require repairing inputs and recalculating outputs, not arbitrary numbers. Correct-looking colours do not verify values. Recheck unique inputs, three definitions, cell explanations and real file so the layout supports learning rather than unexplained binary decoration.