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 'If p, then q' (p → q).

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What are the components of a conditional statement?

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The components of a conditional statement are the hypothesis (p) and the conclusion (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' (q → p).

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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' (¬q → ¬p).

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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' (¬p → ¬q).

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What is the negation of a statement?

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The negation of a statement is the opposite of the statement, often expressed as 'not' followed by the original statement.

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How do you identify the hypothesis in a conditional statement?

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The hypothesis is the part of the conditional statement that follows 'if'. For example, in 'If it rains, then the ground is wet', 'it rains' is the hypothesis.

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How do you identify the conclusion in a conditional statement?

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The conclusion is the part of the conditional statement that follows 'then'. For example, in 'If it rains, then the ground is wet', 'the ground is wet' is the conclusion.

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What is an example of a conditional statement?

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An example of a conditional statement is: 'If a shape is a square, then it has four equal sides.'

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What is the relationship between a statement and its contrapositive?

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A statement and its contrapositive are logically equivalent, meaning they have the same truth value.