Language Proof and Logic(Philosophy)
posted by Ashley on .
write an informal proof of
Premises: LeftOf(a,b) | RightOf(a,b)
BackOf(a,b) | ~Leftof(a,b)
FrontOf(b,a) | ~RightOf(a,b)
SameCol(c,a) & SameRow(c,b)
State if you use proof by cases.
We want to show that if we make the premises of the argument true, the conclusion must be true. In holding
The first premiss tells us that a is either to the left of b or to the right of b. Let’s
consider each of these possibilities in turn.
1. Assume that a is to the left of b. Then, from the second premise, a must be back
of b, which is the conclusion.
2. Assume that a is to the right of b. Then, from the third premise, b must be front
of a. This is equivalent to saying that a is back of b, which is the conclusion.
Either way, then, the conclusion follows from the premises.