Discrete Mathematics
Kid → expert
If P then Q: kid, student, professor
Explain 'if P then Q' to a 5-year-old, a student and a professor
Quick check · tap an answer to continue
Lesson notes
Key points
- Level one: if you finish your food, you get ice cream; you only broke the promise if you finished and got nothing.
- Level two: the conditional P implies Q is false only when P is true and Q is false; every other row is true.
- Level three: P implies Q is equivalent to not P or Q, so a false premise makes it vacuously true, and it matches its contrapositive.
Takeaway: P → Q is false only when P is true and Q is false.
Quick check: When is the statement P → Q false?
- P false and Q true
- P true and Q false
- P and Q both false
A conditional fails only when a true premise leads to a false conclusion.
A promiseConditionalVacuous truth
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