1.5 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) and a conclusion (then). For example, 'If it rains, then the ground is 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, using 'if and only if.' For example, 'Two lines are perpendicular if and only if they intersect at a right angle.'

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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 is 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 is wet' is 'If it does not rain, then the ground is not 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 reversing them. For example, the contrapositive of 'If it rains, then the ground is wet' is 'If the ground is not wet, then it does not rain.'

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How do you rewrite a statement as a biconditional?

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To rewrite a statement as a biconditional, ensure it can be expressed in the form 'P if and only if Q.' For example, 'Two angles are supplementary if and only if the sum of their measures is 180 degrees.'

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What is the conclusion in a conditional statement?

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The conclusion in a conditional statement is the part that follows the 'then.' For example, in 'If two angles are congruent, then they have the same degree,' the conclusion is 'they have the same degree.'

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What is the hypothesis in a conditional statement?

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The hypothesis in a conditional statement is the part that follows the 'if.' For example, in 'If two angles are congruent, then they have the same degree,' the hypothesis is 'two angles are congruent.'

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What does it mean for two statements to be logically equivalent?

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Two statements are logically equivalent if they have the same truth value in every possible scenario. For example, a conditional statement and its contrapositive are logically equivalent.

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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.