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 hypothesis in a conditional statement?

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The hypothesis is the part of the conditional statement that follows the 'if'. It represents the condition that must be met for the conclusion to be true.

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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'. It represents the result or outcome that follows from the hypothesis.

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What is the converse of a conditional statement?

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The converse of a conditional statement is formed by switching the hypothesis and conclusion. For example, the converse of "If P, then Q" is "If Q, then P."

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What is a biconditional statement?

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A biconditional statement is a statement that combines two conditional statements and is true if both statements are true. It is often written as "P if and only if Q."

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How do you write the contrapositive of a conditional statement?

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The contrapositive of a conditional statement is formed by negating both the hypothesis and conclusion and switching them. For example, the contrapositive of "If P, then Q" is "If not Q, then not P."

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What does it mean for a conditional statement to be true?

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A conditional statement is true unless the hypothesis is true and the conclusion is false. In that case, the statement is false.

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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, meaning they have the same truth value.

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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 equivalent; they can have different truth values.

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Provide an example of a conditional statement.

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If it rains, then the ground will be wet.