Conditional Statements

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What is a conditional statement?

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A conditional statement is an if-then statement that expresses a relationship between two propositions, typically written in the form p→q, where p is the hypothesis and q is the conclusion.

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What is the converse of a conditional statement p→q?

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The converse of a conditional statement p→q is q→p.

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What is the inverse of a conditional statement p→q?

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The inverse of a conditional statement p→q is ∼p→∼q.

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What is the contrapositive of a conditional statement p→q?

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The contrapositive of a conditional statement p→q is ∼q→∼p.

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What does 'biconditional' mean in logic?

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A biconditional statement is a statement that combines two conditional statements, written as 'p if and only if q' (p ↔ q), meaning both p and q are true or both are false.

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How do you form the converse of a statement?

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To form the converse of a statement, you switch the hypothesis and conclusion.

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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; if one is true, the other is also true.

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What is the relationship between a conditional statement and its inverse?

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A conditional statement and its inverse are not logically equivalent; one can be true while the other is false.

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What is an example of a conditional statement?

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If it rains, then the ground will be wet (p→q).

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What is an example of a converse statement?

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If the ground is wet, then it rained (q→p).