Lab 18: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 'if'. It represents the condition that must be true for the conclusion to follow.

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

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What is a counterexample?

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A counterexample is an example that disproves a statement or proposition. It shows that the statement is not always true.

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What does it mean to take the converse of a conditional statement?

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Taking the converse of a conditional statement involves 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 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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How do you rewrite a statement as a conditional statement?

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To rewrite a statement as a conditional statement, identify the condition and the result, and express it in the form 'If [condition], then [result]'.

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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; the truth of one does not guarantee the truth of the other.

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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, expressed as 'P if and only if Q'.