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 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 is 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 a conditional statement "If P, then Q" is "If not P, then not 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 a biconditional statement?

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

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How do you negate a statement?

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To negate a statement, you express the opposite of the original statement. For example, the negation of "x > 3" is "x ≤ 3."

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What is the difference between a conditional statement and a biconditional statement?

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A conditional statement has the form "If P, then Q," while a biconditional statement has the form "P if and only if Q," indicating that both statements are true together.

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What is an example of a conditional statement?

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An example of a conditional statement is: "If it rains, then the ground will be wet."

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What is an example of a contrapositive?

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For the conditional statement "If it is a dog, then it barks," the contrapositive is "If it does not bark, then it is not a dog."

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What is an example of an inverse?

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For the conditional statement "If it is a dog, then it barks," the inverse is "If it is not a dog, then it does not bark."