Rules of inference

wannabeCoastie
Flashcards by wannabeCoastie, updated more than 1 year ago
wannabeCoastie
Created by wannabeCoastie about 6 years ago
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Description

This describes the rules that are needed to imply something.

Resource summary

Question Answer
Argument sequences of statements that end with a conclusion
Valid final of the argument,must follow from the truth from the proceeding statements
Modus ponens (p∧(p → q))→ q
Modus tollens (¬q ∧(p → q))→¬p
Hypothetical syllogism ((p → q)∧(q → r))→ (p → r)
Disjunctive syllogism ((p∨q)∧¬p)→ q
Addition p → (p∨q)
Simplification (p∧q)→ p
Conjunction ((p)∧(q)) → (p∧q)
Conjunction ((p)∧(q)) → (p∧q)
Resolution ((p∨q)∧(¬p∨r))→ (q ∨r)
What is the rule of inference with the sentence? "it is below freezing now. Therefore, it is either below freezing or raining now." This is an argument that uses the addition rule p->(p v q)
State the rule of inference "It is below freezing and raining now. Therefore, it is below freezing now" Simplification rule
State rule of reference "If it rain today, then we will not have a barbecue today. If we do not have a barbecue today then we will have a barbecue tomorrow. Therefore, if it rains today, then we will have a barbecue tomorrow. hypothetical syllogism
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