Conditional Statements

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What is a Conditional Statement?

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A statement that can be written in the form 'If P, then Q', where P is the hypothesis and Q is the conclusion.

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What is the Contrapositive of a Conditional Statement?

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The contrapositive of 'If P, then Q' is 'If not Q, then not P'. It is logically equivalent to the original statement.

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What is the Converse of a Conditional Statement?

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The converse of 'If P, then Q' is 'If Q, then P'. It is not necessarily logically equivalent to the original statement.

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What is the Inverse of a Conditional Statement?

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The inverse of 'If P, then Q' is 'If not P, then not Q'. It is not necessarily logically equivalent to the original statement.

Front

Identify the Hypothesis: 'If it rains, then the ground is wet.'

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The hypothesis is 'it rains'.

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Identify the Conclusion: 'If it rains, then the ground is wet.'

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The conclusion is 'the ground is wet'.

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

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True.

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

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False.

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What is the relationship between a Conditional Statement and its Inverse?

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A conditional statement and its inverse are not logically equivalent.

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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.