What you see: two cells merge into the third: what is in both, in either, in one only, or left over. Behind it: set operation (union, intersection, XOR, difference).
Start here — one guess
Look at this for 20 seconds. The third cell in each row comes from combining the first two. What goes in the empty cell?
If you're not sure how the cells combine yet, good — that's the whole chapter. The one thing to notice: the third cell isn't a copy of either input. It's built from both.
The family in one sentence
Combining: the third cell is the first two cells combined by a set rule — kept, shared, or cancelled.
The cells are made of marks (dots, lines, small shapes). The third cell holds some of the marks from the first two, chosen by one rule. Your whole job is to name the rule.
The four set rules: keep everything (union), keep only the shared marks (intersection), keep the unshared marks (XOR), or remove the second from the first (difference).
What Combining looks like
- The first two cells in a row (or column) are the inputs. The third is the result.
- The result uses the same kind of marks as the inputs — it just keeps a different selection of them.
- Nothing rotates, grows, or moves. The only question is which marks survive.
There are four rules in this family, and they differ only in which marks the result keeps:
- Union (OR) — keep every mark that's in either input.
- Intersection (AND) — keep only marks that are in both.
- XOR — keep marks that are in exactly one input (drop the shared ones).
- Difference — keep the first cell's marks that are not in the second.