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 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 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 is not necessarily 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." It is also not necessarily logically equivalent to the original statement.

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How do you identify the contrapositive of a statement?

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To identify the contrapositive, negate both the hypothesis and conclusion of the original statement and switch their places.

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How do you identify the converse of a statement?

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To identify the converse, switch the hypothesis and conclusion of the original statement without negating them.

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How do you identify the inverse of a statement?

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To identify the inverse, negate both the hypothesis and conclusion of the original statement without switching them.

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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." It is true when both parts are either true or false.