Sets and Sorting
📋 What it is
A SET is a well-defined collection of distinct objects — no duplicates, and order does not matter.
🗣️ Coach says
Everything in discrete math starts with sets. A set is just a group with a clear rule for what belongs — {2, 4, 6} is "even numbers under 7". Two rules matter: no item repeats, and {1,2,3} equals {3,1,2} because order is ignored. UNION (∪) puts two sets together; INTERSECTION (∩) keeps only what they share.
🧠 Memory hook
A set = a bag of DISTINCT things, order ignored. ∪ = "either bag", ∩ = "in BOTH bags".
😂 Giggle
Why did the set feel empty?
Because it had nothing in common with anyone — it was the null set!
😲 Whoa!
A Venn diagram — two overlapping circles — was invented by John Venn in 1880 and is now used everywhere from biology to search engines.
✅ Quick check: A = {1,2,3}, B = {3,4,5}. What is A ∩ B (the intersection)?
Say your answer out loud first — then reveal.
{3} — the only element in BOTH sets.
Intersection keeps exactly the items that appear in both sets.
🪄 Trick question: Is {1, 1, 2, 3} a set with four elements?
Careful — think it through, then reveal.
No — a set has no duplicates, so it is {1, 2, 3}: three elements.
Repeats collapse; each element appears once in a set.
🧪 Try it! (2 minutes)
List the set of "letters in your first name" (no repeats), then intersect it with the letters in a friend’s name.