Logic

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What is a biconditional statement?

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A biconditional statement is a logical statement that combines a conditional statement and its converse, expressed as 'P if and only if Q', meaning both P and Q are true or both are false.

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What is the Law of Detachment in logic?

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The Law of Detachment states that if a conditional statement is true and its hypothesis is true, then the conclusion must also be true.

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What is a conditional statement?

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A conditional statement is a logical statement that has the form 'If P, then Q', where P is the hypothesis and Q is the conclusion.

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What is a counterexample?

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A counterexample is an example that disproves a statement or proposition, showing that it is not universally true.

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What is the Law of Syllogism?

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

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What does it mean for a statement to be logically equivalent?

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Two statements are logically equivalent if they have the same truth value in every possible scenario.

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What is the converse of a conditional statement?

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The converse of a conditional statement 'If P, then Q' is 'If Q, then P'.

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What is the inverse of a conditional statement?

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The inverse of a conditional statement 'If P, then Q' is 'If not P, then not Q'.

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What is the contrapositive of a conditional statement?

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The contrapositive of a conditional statement 'If P, then Q' is 'If not Q, then not P'.

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What is a tautology in logic?

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A tautology is a statement that is always true, regardless of the truth values of its components.