- #1

LCharette

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A1: p→~y

A2: ~r→q

A3: p→~z

A4: x→ q or z

A5: r→x or y

Do I have to take the contrapositive of some of the axioms to begin this proof?

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In summary, using the five given axioms, we can prove that p implies q by taking the contrapositive of A5 and A4, and then using the given axioms to deduce p->q.

- #1

LCharette

- 9

- 0

A1: p→~y

A2: ~r→q

A3: p→~z

A4: x→ q or z

A5: r→x or y

Do I have to take the contrapositive of some of the axioms to begin this proof?

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- #2

HallsofIvy

Science Advisor

Homework Helper

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- #3

LCharette

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Conclusions Justifications

1. p Given

2. ~z or ~y All cases

3. ~z Case 1

4. ~x A4

5. ~r A5

6. q A2

An indirect logic proof is a way of proving a statement by assuming its opposite and showing that it leads to a contradiction. This allows us to conclude that the original statement must be true.

The first step in an indirect logic proof is to assume the opposite of the statement you are trying to prove. Then, use logical reasoning and previously established theorems or axioms to arrive at a contradiction.

The purpose of an indirect logic proof is to prove a statement that may be difficult to prove directly. It allows us to use indirect reasoning and arrive at a conclusion without having to provide a direct logical path.

Some tips for writing an indirect logic proof include clearly stating the statement you are trying to prove, carefully choosing your initial assumption, and organizing your proof in a logical and clear manner.

Yes, some common mistakes to avoid when writing an indirect logic proof include not fully exploring all possible outcomes of your initial assumption, making incorrect logical jumps, and not clearly stating your reasoning at each step.

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