Conditional Statements & Counterexample Practice

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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 will be wet.'

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What is the hypothesis in a conditional statement?

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The hypothesis is the part of the conditional statement that follows the word 'if'. It represents the condition that must be met.

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What is the conclusion in a conditional statement?

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The conclusion is the part of the conditional statement that follows the word 'then'. It represents the result or outcome of the hypothesis being true.

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What is the inverse of a conditional statement?

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The inverse of a conditional statement negates both the hypothesis and the conclusion. For example, the inverse of 'If it rains, then the ground will be wet' is 'If it does not rain, then the ground will not be wet.'

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What is the converse of a conditional statement?

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The converse of a conditional statement switches the hypothesis and conclusion. For example, the converse of 'If it rains, then the ground will be wet' is 'If the ground is wet, then it rains.'

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What is the contrapositive of a conditional statement?

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The contrapositive of a conditional statement switches and negates both the hypothesis and conclusion. For example, the contrapositive of 'If it rains, then the ground will be wet' is 'If the ground is not wet, then it does not rain.'

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What is a counterexample?

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A counterexample is an example that disproves a statement or conjecture. For instance, if the statement is 'All birds can fly', a counterexample would be 'Penguins cannot fly.'

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How do you prove a conjecture is false?

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To prove a conjecture is false, you can provide a counterexample that shows the conjecture does not hold true in all cases.

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What does it mean to negate a statement?

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To negate a statement means to state the opposite of that statement. For example, the negation of 'It is raining' is 'It is not raining.'

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What is the difference between inductive reasoning and deductive reasoning?

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Inductive reasoning involves making generalizations based on specific observations, while deductive reasoning involves applying general principles to reach a specific conclusion.