Inductive and Deductive Reasoning

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What is inductive reasoning?

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Inductive reasoning is a type of reasoning that involves making generalizations based on specific observations or patterns.

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What is deductive reasoning?

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Deductive reasoning is a logical process where a conclusion is reached based on the concordance of multiple premises that are generally assumed to be true.

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Provide an example of inductive reasoning.

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All observed swans are white; therefore, all swans are white.

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Provide an example of deductive reasoning.

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All humans are mortal. Socrates is a human. Therefore, Socrates is mortal.

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What is a key characteristic of inductive reasoning?

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Inductive reasoning often leads to conclusions that are probable but not guaranteed.

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What is a key characteristic of deductive reasoning?

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Deductive reasoning leads to conclusions that are logically certain if the premises are true.

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What does it mean for a definition to be reversible?

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A definition is reversible if the terms can be interchanged without losing meaning.

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What is the contrapositive of a conditional statement?

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The contrapositive of a statement 'If P, then Q' is 'If not Q, then not P'.

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What is a pattern in mathematics?

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A pattern is a repeated or predictable sequence of numbers or shapes.

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How do you identify the next numbers in a numerical pattern?

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To identify the next numbers, determine the rule or operation that generates the sequence.