Help with indirect logic proof please

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
Using the five axioms below prove: p→q

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
Yes, that would be the simplest thing to do. The very first "axiom" gives you p-> ~y but there is no "~y-> " so you cannot continue directly. However, you do have "A5: r->x or y which has contrapositive ~(x or y)= (~x) and (~y)->~r and then both "A2: ~r-> q" and "A4: x-> q or z".
 
  • #3
Am I on the right track with this?

Conclusions Justifications
1. p Given
2. ~z or ~y All cases
3. ~z Case 1
4. ~x A4
5. ~r A5
6. q A2
 

1. What is an indirect logic proof?

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.

2. How do I start an indirect logic proof?

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.

3. What is the purpose of using an indirect logic proof?

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.

4. What are some tips for writing an indirect logic proof?

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.

5. Are there any common mistakes to avoid when writing an indirect logic proof?

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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