# Twenty application bridges · two per day

These invented prompts vary context without presenting real survey findings. Each says exactly what is counted. Replace a name or setting freely if the set/branch logic remains valid. A learner can supply their own **fictional** domain, never private classmate data.

| Day | Domain A and method | Domain B and method |
| --- | --- | --- |
| 1 | Museum visitors selecting audio or text guide: subtract visitors using both. | Community club enrolments in dance or chess: subtract dual membership. |
| 2 | Repair-café visitors: known union and two interests reveal overlap. | Library borrowers: known “at least one” and total reveal neither. |
| 3 | Three elective interests: pairwise totals include all-three students. | Three public-transport route preferences in a **fictional** survey: centre added back once. |
| 4 | Choose exactly one workshop from indoor or outdoor list: disjoint sum. | Pick one podcast episode from two nonoverlapping shelves: disjoint sum. |
| 5 | Sports sign-ups with two activities and shared names: fresh transfer only after G. | One booking from two exclusive time windows: addition, not pairs. |
| 6 | Museum label shape and caption: one from each stage. | Game avatar colour and frame: product only if all pairs allowed. |
| 7 | Choose one display route; within route choose format and voice: branch products then sum. | Choose one community announcement format; within each choose dimensions: same branch structure. |
| 8 | Environmental-interest clubs: reconstruct seven regions to test claimed counts. | Three book genres: a pair intersection cannot be smaller than the triple. |
| 9 | Festival ticket interests overlap; seat choice branches do not: contrast methods. | Stationery label stages vs one-section choice: product vs sum. |
| 10 | After H/I, compare a fresh three-service interest count by regions. | After H/I, compare two exclusive design routes with paired attributes. |

The “application” is a model of counting, not a statement about how people actually behave or which mode suits a learner. No claim is made about accessibility preferences, demographics, culture or demand.