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). For example, 'If it rains, then the ground is wet.'

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Identify the hypothesis in the statement: 'If it is snowing, then it is cold.'

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The hypothesis is 'It is snowing.'

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Identify the conclusion in the statement: 'If it is snowing, then it is cold.'

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The conclusion is 'It is cold.'

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What is the converse of the statement: 'If it rains, then the ground is wet.'?

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The converse is 'If the ground is wet, then it rains.'

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What is the inverse of the statement: 'If it rains, then the ground is wet.'?

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

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What is 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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True or False: The contrapositive of a conditional statement is logically equivalent to the original statement.

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True

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True or False: The converse of a conditional statement is logically equivalent to the original statement.

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False

Front

What is the definition of 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.'

Front

Provide an example of a biconditional statement.

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An example of a biconditional statement is: 'A figure is a square if and only if it has four equal sides.'