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 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 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."

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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."

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What is the conclusion of a conditional statement?

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The conclusion is the part that follows the 'then' in a conditional statement. For example, in "If P, then Q," Q is the conclusion.

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How do you form the contrapositive of the statement: 'If it rains, then the ground is wet'?

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The contrapositive is: 'If the ground is not wet, then it does not rain.'

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How do you form the inverse of the statement: 'If you study, then you will pass'?

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The inverse is: 'If you do not study, then you will not pass.'

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How do you form the converse of the statement: 'If a shape is a square, then it is a rectangle'?

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The converse is: 'If a shape is a rectangle, then it is a square.'

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What is an example of a conditional statement in geometry?

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An example is: 'If a figure is a triangle, then it has three 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; if one is true, the other is also true.