Conditional Statements

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What is a conditional statement?

Back

A logical statement that has two parts: a hypothesis and a conclusion, typically expressed in the form 'If P, then Q'.

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What is the hypothesis in a conditional statement?

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The part of the statement that follows 'if'. It is the condition that must be true for the conclusion to follow.

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What is the conclusion in a conditional statement?

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The part of the statement that follows 'then'. It is the result that follows if the hypothesis is true.

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Rewrite the statement in if-then form: 'A quadrilateral is a figure with four sides.'

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If a figure is a quadrilateral, then it has four sides.

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What is the converse of a conditional statement?

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The statement formed by reversing the hypothesis and conclusion. For example, the converse of 'If P, then Q' is 'If Q, then P'.

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What is a biconditional statement?

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

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When can a biconditional statement be true?

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When both the original conditional statement and its converse are true.

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What is the contrapositive of a conditional statement?

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The statement formed by negating both the hypothesis and conclusion and reversing them. For example, the contrapositive of 'If P, then Q' is 'If not Q, then not P'.

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What is an example of a conditional statement?

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If it rains, then the ground will be wet.

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What is an example of a converse statement?

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If the ground is wet, then it rained.