5 Fifth Week Flashcards
What is the Las Vegas Rule?
“What happens in a mini-proof stays in a mini-proof.”
In more detail …
Suppose you use a mini-proof to prove some statement by conditional proof or reductio ad absurdum. Once this has been done, you can’t use statements inside the mini-proof as premises for later inferences.
When you use conditional proof in a natural deduction proof, what is the top statement in the mini-proof? What is bottom statement?
The antecedent to your conditional goes at the top. The consequent goes at the bottom.
What does it mean to say that two statements are “logically equivalent”?
It means that the two statements logically must have the same truth value. If one of them is true, so is the other. If one of them is false, so is the other.
When you use reductio ad absurdum in a natural deduction proof, what is the top statement in the mini-proof? What goes at the bottom of the mini-proof?
If you’re trying to prove P, start your mini-proof by putting ~P at the top.
If you’re trying to prove ~P, start your mini-proof by putting P at the top.
The bottom two statements in the mini-proof will be two statements, one of which is the negation of the other.
