Reasoning and Proofs (Honors Geometry)

Front

What is a conditional statement?

Back

A conditional statement is an if-then statement that expresses a relationship between two propositions, where the first proposition (hypothesis) implies the second (conclusion).

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What is the contrapositive of a conditional statement?

Back

The contrapositive of a conditional statement '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 inverse of a conditional statement?

Back

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 converse of a conditional statement?

Back

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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How do you identify the hypothesis in a conditional statement?

Back

The hypothesis is the part of the conditional statement that follows 'if'. For example, in 'If it rains, then the ground is wet', 'it rains' is the hypothesis.

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How do you identify the conclusion in a conditional statement?

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The conclusion is the part of the conditional statement that follows 'then'. For example, in 'If it rains, then the ground is wet', 'the ground is wet' is the conclusion.

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What is the relationship between a statement and its contrapositive?

Back

A statement and its contrapositive are logically equivalent, meaning if one is true, the other is also true.

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What is the relationship between a statement and its inverse?

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A statement and its inverse are not logically equivalent; one can be true while the other is false.

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What is the relationship between a statement and its converse?

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A statement and its converse are not logically equivalent; one can be true while the other is false.

Front

Provide an example of a conditional statement.

Back

If a figure is a square, then it has four equal sides.