Conditional Statements & Logic

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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 in the form 'p if and only if q', meaning both p and q are true or both are false.

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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 the hypothesis and conclusion.

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What does the symbol '→' represent in logic?

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The symbol '→' represents a conditional statement, indicating that if the first statement (hypothesis) is true, then the second statement (conclusion) is also true.

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What is a conditional statement?

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A conditional statement is a logical statement that has the form 'if p, then q', where p is the hypothesis and q is the conclusion.

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What is the difference between a conditional statement and a biconditional statement?

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A conditional statement has the form 'if p, then q', while a biconditional statement has the form 'p if and only if q', meaning both statements are equivalent.

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True or False: The contrapositive of a statement is logically equivalent to the original statement.

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True. The contrapositive of a statement is always logically equivalent to the original statement.

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What is the truth value of a statement that is false?

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The truth value of a false statement is 'false'.

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If a polygon is a quadrilateral, then it is a trapezoid. What is the contrapositive of this statement?

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If a polygon is not a trapezoid, then it is not a quadrilateral.