Question

exercise 5.8
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)
conclusion BackOf(a,b)
State if you use proof by cases.

Answer 1

We want to show that if we make the premises of the argument true, the conclusion must be true. In holding
premise

Answer 2

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.