Conditional Statement Practice

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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). For example, 'If it rains, then I will stay indoors.'

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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.' For example, the inverse of 'If it rains, then I will stay indoors' is 'If it does not rain, then I will not stay indoors.'

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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.' For example, the converse of 'If it rains, then I will stay indoors' is 'If I stay indoors, then it rains.'

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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.' For example, the contrapositive of 'If it rains, then I will stay indoors' is 'If I do not stay indoors, then it does not rain.'

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What is a counterexample?

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A counterexample is an example that disproves a statement or proposition. For instance, if the statement is 'All birds can fly,' a counterexample would be 'ostrich' or 'penguin.'

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What does it mean if a statement is true?

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A statement is true if it accurately reflects reality or a fact. In logic, a true statement is one that holds under the given conditions.

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What does it mean if a statement is false?

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A statement is false if it does not accurately reflect reality or a fact. In logic, a false statement is one that does not hold under the given conditions.

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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 parts are either true or false.

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

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The truth value of a conditional statement 'If P, then Q' is false only when P is true and Q is false. In all other cases, it is true.

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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, meaning they have the same truth value.