Deductive Reasoning

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What is Deductive Reasoning?

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Deductive reasoning is a logical process where a conclusion is reached by applying general principles to specific cases. It starts with a general statement or hypothesis and examines the possibilities to reach a specific, logical conclusion.

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What is the Law of Detachment?

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The Law of Detachment states that if a conditional statement (if p, then q) is accepted as true, and the antecedent (p) is true, then the consequent (q) must also be true.

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What is the Law of Syllogism?

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The Law of Syllogism states that if the first statement implies a second statement (if p, then q) and the second statement implies a third statement (if q, then r), then the first statement implies the third statement (if p, then r).

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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) and a conclusion (then). It is often written in the form 'If p, then 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'. It switches the hypothesis and conclusion.

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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'. It negates both the hypothesis and conclusion.

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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 switches and negates both the hypothesis and conclusion.

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How do you identify a valid argument using Deductive Reasoning?

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A valid argument in deductive reasoning is one where if the premises are true, the conclusion must also be true. This can be checked using laws like Detachment and Syllogism.

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What is an example of the Law of Detachment?

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If it rains, then the ground will be wet. It is raining. Therefore, the ground is wet.

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What is an example of the Law of Syllogism?

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If it is a holiday, then the store is closed. If the store is closed, then I will go shopping tomorrow. Therefore, if it is a holiday, then I will go shopping tomorrow.