Mathematics from zero
Logic and sets: build a reasoning kit
Knowing the AND, OR, NOT rules is not the same as wielding them. In this project you turn the whole unit into a small paper kit — your own truth tables and set diagrams — and then use it to settle real yes-or-no questions, the way logic is actually used.
Turn the unit’s ideas into a reusable tool: write out the truth tables for AND, OR, and NOT, build two real sets and combine them, and then apply the kit to decide three everyday questions, showing each truth value or membership step.
Build a one-page logic-and-sets reference kit by hand, then use it to resolve three real yes-or-no questions — showing every truth value and membership step, not just the final answer.
- The six-sentence table correctly separates statements from non-statements, with a 1 or 0 truth value on every statement and at least one of each required kind (a non-statement and a false statement).
- All three truth tables are complete and correct: AND true in one row only, OR false in one row only, NOT flipping both rows.
- The three combined statements each show the right final truth value, traceable back to a row of your tables.
- The union and intersection are correct for your two sets — shared elements counted once, intersection no larger than the smaller set, union no smaller than the larger set — with the size of each written next to it.
- Add a fourth combination using two connectives at once, such as NOT (A AND B), and work out its truth value step by step from the inside out.
- Find a real pair of overlapping groups (people who like tea, people who like coffee) and use union and intersection to answer 'how many like at least one' and 'how many like both'.
- Write a half-page note explaining, in your own words, why set membership is a yes-or-no question just like a truth value — and why that makes union behave like OR and intersection behave like AND.
- Make a blank version of your kit (empty truth tables and two empty set brackets) and hand it to a friend with three fresh sentences and groups, so they can run the same process cold.
This is logic as a working tool, not a list of rules. You classified real sentences as statements or not, built the truth tables that decide every AND, OR, and NOT, and combined real sets by union and intersection — then watched the two halves of the unit turn out to be the same machinery: membership is yes-or-no like a truth value, union is the ‘or’ of sets, and intersection is the ‘and’. Once the kit is on paper, every future yes-or-no question becomes a step you can check.