Conditional and Biconditional Statements

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What is a conditional statement?

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A conditional statement is a logical statement that has two parts: a hypothesis (if part) and a conclusion (then part). It is often written in the form "If P, then Q."

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What is the hypothesis in a conditional statement?

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The hypothesis is the part of the conditional statement that follows the 'if'. It represents the condition that must be true for the conclusion to follow.

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What is the conclusion in a conditional statement?

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The conclusion is the part of the conditional statement that follows the 'then'. It represents the result or outcome that follows from the hypothesis.

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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'. It switches the hypothesis and conclusion.

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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'. It negates both the hypothesis and conclusion.

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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'. It switches and negates both the hypothesis and conclusion.

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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, written as 'P if and only if Q'. It is true when both parts are either true or false.

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Provide 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 for a statement to be true?

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A statement is true if it accurately reflects reality or a logical condition.

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What does it mean for a statement to be false?

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A statement is false if it does not accurately reflect reality or a logical condition.