Rules of Inference

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What is a rule of inference?

Back

A rule of inference is a logical rule that is used to deduce one statement from another. It allows for the derivation of conclusions from premises.

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What is Modus Ponens?

Back

Modus Ponens is a rule of inference that states if 'P implies Q' (P → Q) is true and P is true, then Q must also be true.

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What is Modus Tollens?

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Modus Tollens is a rule of inference that states if 'P implies Q' (P → Q) is true and Q is false (¬Q), then P must also be false (¬P).

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What is the Law of Syllogism?

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The Law of Syllogism states that if 'P implies Q' (P → Q) and 'Q implies R' (Q → R) are both true, then 'P implies R' (P → R) is also true.

Front

What is the Law of Contraposition?

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The Law of Contraposition states that 'P implies Q' (P → Q) is logically equivalent to 'not Q implies not P' (¬Q → ¬P).

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What is the Absorption Law?

Back

The Absorption Law states that 'P and (P or Q)' (P ∧ (P ∨ Q)) is equivalent to P, and 'P or (P and Q)' (P ∨ (P ∧ Q)) is also equivalent to P.

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What is the Disjunctive Syllogism?

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Disjunctive Syllogism is a rule of inference that states if 'P or Q' (P ∨ Q) is true and P is false (¬P), then Q must be true.

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What is the Conjunction Rule?

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The Conjunction Rule states that if P is true and Q is true, then 'P and Q' (P ∧ Q) is also true.

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What is the Simplification Rule?

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The Simplification Rule states that if 'P and Q' (P ∧ Q) is true, then P is true and Q is true.

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What is the Addition Rule?

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The Addition Rule states that if P is true, then 'P or Q' (P ∨ Q) is also true, regardless of the truth value of Q.