Conditional Statements Review

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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 a counterexample?

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A counterexample is an example that disproves a statement or proposition. For a conditional statement, a counterexample shows that the hypothesis can be true while the conclusion is false.

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What is the conclusion in a conditional statement?

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The conclusion is the part of the conditional statement that follows the 'then' clause. It represents the outcome that is asserted if the hypothesis is true.

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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." It switches the hypothesis and conclusion.

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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." It negates both the hypothesis and conclusion.

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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." It switches and negates both the hypothesis and conclusion.

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How do you identify a counterexample for the statement: 'If an animal is furry, then it is a hamster'?

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A counterexample would be any furry animal that is not a hamster, such as a cat.

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What is the relationship between a 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 statement and its converse?

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

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

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If the ground is wet, then it rains.