Conditional 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) and a conclusion (then). For example, "If it rains, then the ground will be wet."

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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, typically expressed as "p if and only if q." For example, "An angle is a right angle if and only if its measure is 90°."

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What is the converse of a conditional statement?

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The converse of a conditional statement is formed by reversing the hypothesis and conclusion. For example, the converse of "If it rains, then the ground will be wet" is "If the ground is wet, then it rains."

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What is the inverse of a conditional statement?

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The inverse of a conditional statement is formed by negating both the hypothesis and conclusion. For example, the inverse of "If it rains, then the ground will be wet" is "If it does not rain, then the ground will not be wet."

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What is the contrapositive of a conditional statement?

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The contrapositive of a conditional statement is formed by negating both the hypothesis and conclusion and then reversing them. For example, the contrapositive of "If it rains, then the ground will be wet" is "If the ground is not wet, then it does not rain."

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What is the hypothesis in a conditional statement?

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The hypothesis is the part of a conditional statement that follows the 'if.' For example, in "If it rains, then the ground will be wet," the hypothesis is "it rains."

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What is the conclusion in a conditional statement?

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The conclusion is the part of a conditional statement that follows the 'then.' For example, in "If it rains, then the ground will be wet," the conclusion is "the ground will be wet."

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What does it mean if a conditional statement is true?

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A conditional statement is true unless the hypothesis is true and the conclusion is false. For example, "If it rains, then the ground is wet" is false only if it rains and the ground is not wet.

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What is a negation in logic?

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A negation is the opposite of a statement. For example, the negation of "It is raining" is "It is not raining."

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How do you determine the truth value of a conditional statement?

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To determine the truth value of a conditional statement, check if the hypothesis is true and if the conclusion follows. If the hypothesis is true and the conclusion is false, the statement is false; otherwise, it is true.