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 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 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 true even if the original statement is true.

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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 true.

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What does it mean if a statement is true?

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A statement is true if it accurately reflects reality or a fact.

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What does it mean if a statement is false?

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A statement is false if it does not accurately reflect reality or a fact.

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Provide an example of a valid counterexample for the statement: 'If it rains, then the ground is wet.'

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A valid counterexample would be a situation where it rains but the ground is not wet, such as when the ground is covered.

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What is the difference between a hypothesis and a conclusion in a conditional statement?

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The hypothesis is the 'if' part of the statement, while the conclusion is the 'then' part. For example, in 'If it is sunny, then I will go outside,' 'it is sunny' is the hypothesis and 'I will go outside' is the conclusion.

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What is a logical equivalence?

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Two statements are logically equivalent if they have the same truth value in every possible scenario.