Conditional Statements

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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). It is often written in the form 'If P, then Q.'

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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.'

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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.'

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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.'

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True or False: The converse of a true statement is always true.

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False. The converse of a true statement may not be true.

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

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

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Write the converse of: 'If it rains, then the ground is wet.'

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If the ground is wet, then it rains.

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Write the inverse of: 'If you study, then you will pass the test.'

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If you do not study, then you will not pass the test.

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Write the contrapositive of: 'If you are a cat, then you are a mammal.'

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If you are not a mammal, then you are not a cat.

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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, written as 'P if and only if Q.'