TopoWeave

A name with possibilities.

Overlay two small masks

The exercise overlays two fictional two-by-three masks. Mask A marks the upper-left, upper-centre and lower-right cells. Mask B marks the upper-centre, lower-left and lower-right cells. A marked cell has value 1 and an unmarked cell value 0. Both masks use the same grid, so positions correspond directly without any rescaling or alignment step.

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Source masksTwo-by-three binary masksA: 1 1 0 / 0 0 1B: 0 1 0 / 1 0 1Three marked cells in each1 = marked; 0 = unmarked

01

Write the two masks as rows

Record A as upper row 1,1,0 and lower row 0,0,1. Record B as upper row 0,1,0 and lower row 1,0,1. Each mask contains three marked cells. Keep the row order and column order fixed when comparing them. The shared upper-centre and lower-right positions are visible in both lists, while upper-left belongs only to A and lower-left only to B. Writing the rows alongside the diagram provides a second representation that makes the example easier to verify without relying on the appearance of the coloured cells.

UnionMark positions present in eitherUpper row: 1 1 0Lower row: 1 0 1Union count: four3 + 3 − 2 = 4

02

Compare union and intersection

For the union of these two masks, mark a position when either mask contains a 1. The resulting rows are 1,1,0 and 1,0,1, giving four marked cells. For the intersection, mark only positions where both masks contain a 1. Its rows are 0,1,0 and 0,0,1, giving two marked cells. The counts satisfy three plus three minus two equals four: add both mask counts and subtract the shared cells counted twice. The arithmetic describes this explicit grid; it does not attach any real-world significance to the resulting area.

IntersectionMark positions present in bothUpper row: 0 1 0Lower row: 0 0 1Intersection count: twoCheck positions as well as totals

03

Keep the source layers with the composite

Use a worksheet containing the two original row lists, the chosen operation and the result. Include a small legend defining 1 as marked and 0 as unmarked. Check each of the six positions rather than only the final count, because an incorrect arrangement can still have four marked cells. Preserve separate union and intersection versions so their purposes remain clear. A later design can assign a visual treatment to each view, but the operation and source masks should stay available when someone needs to understand how the composite was produced.

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