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 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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What is an 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 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" (P iff Q).

Front

Identify the hypothesis and conclusion in the statement: "If it rains, then the ground is wet."

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Hypothesis: It rains; Conclusion: The ground is wet.

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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.

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What is the relationship between a conditional statement and its converse?

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

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Provide an example of a conditional statement.

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Example: "If a shape is a square, then it has four equal sides."

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Provide an example of a converse statement.

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Example: "If a shape has four equal sides, then it is a square."