Propositional Logic
📋 What it is
A proposition is a statement that’s true or false; connectives (and, or, not, if-then) join them into bigger statements.
🗣️ Coach says
A proposition is any sentence you can call true or false (“it’s Tuesday”). Connectives glue them together. The trickiest is “if-then”: “if it rains, the ground is wet” — it only breaks its promise when it rains AND the ground is dry.
🧠 Memory hook
If-then breaks its promise ONLY when the “if” happens but the “then” doesn’t.
😂 Giggle
Why did the Venn diagram feel included?
Because it was in the intersection of two great groups!
😲 Whoa!
The “if-then” (implication) confuses everyone at first: “if pigs fly, then 2+2=5” is counted TRUE in logic, because the “if” never happens so the promise is never broken.
✅ Quick check: “If you finish your homework, you can play.” The only broken-promise case is…?
Say your answer out loud first — then reveal.
You finished your homework BUT were not allowed to play — that’s the one case that breaks the if-then.
An if-then is false only when the “if” is true and the “then” is false.
🧪 Try it! (2 minutes)
Write an “if-then” promise, then list the four cases (if yes/no × then yes/no) and circle the only broken one.