Conditional & Biconditional Statements

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What is a biconditional statement?

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A biconditional statement is a statement that combines a conditional statement and its converse, expressed as 'P if and only if Q'. It is true when both the original statement and its converse are 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 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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When is a biconditional statement true?

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A biconditional statement is true when both the original conditional statement and its converse are true.

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What is an example of a biconditional statement?

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An example of a biconditional statement is: 'An angle is a right angle if and only if its measure is 90 degrees'.

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What does it mean if a statement is a conjecture?

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A conjecture is a statement that is believed to be true based on observations but has not yet been proven.

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What is the relationship between a conditional statement and its contrapositive?

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A conditional statement and its contrapositive are logically equivalent; if one is true, the other is also true.

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What is the relationship between a conditional statement and its inverse?

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A conditional statement and its inverse are not logically equivalent; one can be true while the other is false.