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Language Proof and Logic(Philosophy)

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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.

  • Language Proof and Logic(Philosophy) -

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

  • Language Proof and Logic(Philosophy) -

    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.

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