Conditional Statements & Related Conditionals

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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 the ground is wet.'

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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 the ground is wet' is 'If it does not rain, then the ground is not wet.'

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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 the ground is wet' is 'If the ground is wet, 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 the ground is wet' is 'If the ground is not wet, then it does not rain.'

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What is an acute angle?

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An acute angle is an angle that measures less than 90 degrees.

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What is an equilateral triangle?

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An equilateral triangle is a triangle in which all three sides are of equal length.

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What is the truth value of a conditional statement?

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The truth value of a conditional statement indicates whether the statement is true or false. A conditional statement is false only when the hypothesis is true and the conclusion is false.

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Provide an example of a counterexample in conditional statements.

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A counterexample is an example that disproves a statement. For instance, in the statement 'If an angle is acute, then it measures 30 degrees,' a counterexample is an angle measuring 20 degrees, which is acute but does not measure 30 degrees.

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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.

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

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A conditional statement and its converse are not necessarily logically equivalent; they can have different truth values.