Conditional and Biconditional Statements

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What is a conditional statement?

Back

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 a converse statement?

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The converse of a conditional statement 'If P, then Q' is 'If Q, then P'.

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What is a biconditional statement?

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A biconditional statement is a logical statement that combines a conditional and its converse, expressed as 'P if and only if Q'.

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What is a contrapositive statement?

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The contrapositive of a conditional statement 'If P, then Q' is 'If not Q, then not P'.

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What is an inverse statement?

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The inverse of a conditional statement 'If P, then Q' is 'If not P, then not Q'.

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How do you form the converse of the statement: 'If a polygon is a quadrilateral, then it is a trapezoid'?

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The converse is: 'If a polygon is a trapezoid, then it is a quadrilateral.'

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How do you form the contrapositive of the statement: 'If a polygon is a quadrilateral, then it is a trapezoid'?

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The contrapositive is: 'If a polygon is not a trapezoid, then it is not a quadrilateral.'

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How do you form the inverse of the statement: 'If a polygon is a quadrilateral, then it is a trapezoid'?

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The inverse is: 'If a polygon is not a quadrilateral, then it is not a trapezoid.'

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What is the biconditional for the statement: 'A right angle is an angle with 90 degrees'?

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The biconditional is: 'An angle is a right angle if and only if it has 90 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; if one is true, the other is also true.