- #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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In summary, when approaching an indirect logic proof, start by assuming the opposite of the conclusion and reach a contradiction using common logical rules. An indirect proof is usually used when a direct proof is not possible or when a statement involves negations or contradictions. Common mistakes to avoid include assuming the original conclusion and using invalid logical rules. Indirect logic proofs can also be applied in other fields of study such as mathematics, computer science, and philosophy.

- #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

CompuChip

Science Advisor

Homework Helper

- 4,309

- 49

You can also solve it using the tautology (r or ~r) and using or-elimination (i.e. assuming p, show that r -> q and ~r -> q).

There are a few steps to follow when approaching an indirect logic proof. First, start by assuming the opposite of the conclusion you are trying to prove. Then, use logical rules and principles to reach a contradiction. Finally, conclude that the opposite of the assumption you made must be true, which proves the original conclusion.

Some common logical rules used in indirect proofs include the law of non-contradiction, the law of excluded middle, and the principle of double negation. These rules allow you to manipulate statements and reach a contradiction, ultimately proving the original conclusion.

An indirect proof is typically used when a direct proof is not possible or is too complex. If you are having trouble finding a direct proof for a statement, an indirect proof may be a good approach to try. Additionally, if a statement involves negations or contradictions, an indirect proof is usually the best method.

One common mistake in an indirect proof is assuming the original conclusion instead of its opposite. Remember to start by assuming the opposite of the conclusion and work towards a contradiction. Another mistake is using invalid logical rules or making incorrect deductions. Make sure to carefully apply logical principles and check for any inconsistencies in your proof.

Yes, indirect logic proofs are commonly used in various fields of study such as mathematics, computer science, and philosophy. These proofs allow for a rigorous and logical approach to problem-solving and can be applied to many different situations and scenarios.

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