Subsection 3.5.5 Disjunctive Syllogism Proof Example: Who Drives Me?
Who Drives Me?Next, let’s use natural deduction to prove an extension of one of the claims that we’ve already proved with a truth table. We’ll pick up where we left off with the ex Who Drives Me example. We’ll assign the following names to basic statements:
J: John must drive me to the store.
M: Mary must drive me to the store.
L: John will be late for work.
G: Mary must buy gas.
Y: Mary must have money.
W: Mary must work at a paying job.
(Note that we’ve simplified reality to assert that Mary must have a paying job in order to have money.)
Our premises will be:
J M John or Mary must drive me to the store.
J L If John drives me to the store, he will be late for work.
L John cannot be late for work.
M G If Mary must drive me to the store, she must buy gas.
G Y If Mary must buy gas, she must have money.
Y W If Mary must have money, then she must work at a paying job.
We’d like to prove:
W Mary must work at a paying job.
Again, you should try to do this proof yourself.
You can also watch our video, which will outline a strategy for creating a proof
On the next page, you’ll find a summary of the approach that is described in the video.
